The average power output by the athlete during the climb is equal to 321 joules per second or 321 watts.
In physics, power is defined to be work W over elapsed time t (P = W/t). Work is defined to be force F times displacement x (W = F · x). Weight is the force of gravity (Fg) and is equal to mass m times acceleration due to gravity g (Fg = m · g).
We are given that the athlete's mass is 82 kg and the acceleration due to Earth's gravity is 9.8 m/s², hence the athlete's weight is equal to 803.6 newtons. Also, the height of each of the 60 steps is 0.32 meters. The work done by the athlete then is Fg · x = 803.6 · (60 · 0.32) = 15,492.12 joules. Therefore, in 48 seconds the work done by the athlete is equal to 15,492.12 joules.
However, we haven't divide the work done by the elapsed time. The standard unit of power is watt (W — not to be confused with work W), and 1 watt is equal to 1 joule per 1 second (1 W = 1 J/s). We only need to divide the work done by 48 to get the average power output as follows:
15,492.12/48 = 321 J/s = 321 W.
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Two parallel plates having charges of equal magnitude but opposite sign are separated by 11. 0 cm. Each plate has a surface charge density of 49. 0 nC/m2. A proton is released from rest at the positive plate. (a) Determine the magnitude of the electric field between the plates from the charge density
The magnitude of the electric field between the plates from the charge density is 0.0536 × 10⁵ N/C.
Separation between two plate is 11 cm and change density б is 49 nC/m². Magnitude of the electric field is E = б/2Е₀
E = 49 × 10⁵ /885. the electromagnetic field that surrounds electrically charged particles and pulls or pulls all other charged particles in the field them, is known as an electric field (or E-field). It can also refer to the physical field surrounding a system of charged particles. The biggest size and direction of an object are described by its magnitude. Magnitude is a factor that is shared by both scalar and vector values. We are aware that by definition, scalar quantities are those with only magnitude.
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which one of the following is the smallest mass? 0.052g or 5.2mg or 5.2cg or 5.2*10^(-4) kg
Out of the given options, the smallest mass is the 5.2 mg.
To compare the given masses, we should convert them in the same unit. Lets convert them in kg unit.
Mass of the first object, M₁ = 0.052 g = 52 × 10⁻⁶ kg.
Mass of the second object, M₂ = 5.2 mg = 5.2 × 10⁻⁶ kg
Mass of the third object, M₃ = 5.2 g = 52 × 10⁻⁶ kg
Mass of the fourth object, M₄ = 5.2 × 10⁻⁴ kg = 520 × 10⁻⁶ kg
After converting them in the same mass unit, which is kg, we can see that M₂ = 5.2 × 10⁻⁶ kg is the smallest mass.
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Two masses m1 = 15 kg amd m2 = 25 kg are joined by connecting a rod of length 0.8 m. Determine the
distance of the CM of the system from the m1 if a.) the connecting rod is massless, and b.) the connecting
rod is a uniform rod of mass 15 kg.
(a) The center mass when the connecting rod is massless is 0.5 m.
(b) The center mass when the connecting rod has a mass of 15 kg is 0.47 m.
What is the center mass of mass m1?The center mass of m1 is calculated by applying the following formula for center of gravity.
Cm = ( m1x₀ + m2x₁ ) / ( m1 + m2 )
when the connecting rod is massless,
Cm = ( 15kg x 0 + 25kg x 0.8 m ) / ( 15 kg + 25 kg )
Cm = 0.5 m
when the connecting rod has a mass of 15 kg;
Cm = ( 15 kg x 0 + 15 kg x 0.4 m + 25 x 0.8 m ) / ( 15 kg + 15kg + 25 kg )
Cm = 0.47 m
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Find the speed of a sound wave in air when the temperature of the air is 17.3 °C
The speed of a sound wave in air is 341.33 m/s when the temperature of the air is 17.3 °C.
What is sound?In terms of physics, sound is a vibration that travels through a transmission medium like a gas, liquid, or solid as an acoustic wave. Sound is the reception of these waves and the brain's perception of them in terms of human physiology and psychology.
At 0° C, speed of sound in air is = 331 m/s
speed of sound ∝ √T
Hence, at 17.3°C, the speed of sound in air is = 331 m/s ×√{(273+17.3)/273}
= 341.33 m/s.
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if these two piles of logs both catch on fire which pile will burn faster
The horizontal pile placed on top of each other like a pyramid will burn faster because the fire has more surface area to ignite, and the vertical pile will have less exposure to the fire. Additionally, the fire in the horizontal pile will be able to spread faster since the logs are in direct contact with each other.
In general, the pile of logs that are placed horizontally on top of each other in a pyramid shape will burn faster compared to the pile that is placed vertically next to each other. The reason for this is that the fire has more surface area to ignite in the horizontal pile, allowing it to spread quickly. Additionally, since the logs in the horizontal pile are in direct contact with each other, the fire is able to jump from one log to another, which further accelerates the burning process. On the other hand, the vertical pile will have less exposure to the fire as it only has one side that is directly exposed to the flames. Therefore, the vertical pile will burn more slowly and steadily, while the horizontal pile will burn faster.
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a rotating cylinder about 10 mi in length and 5.0 mi in diameter is designed to be used as a space colony. with what angular speed must it rotate so the residents on it will experience the same acceleration as that due to gravity on earth?
The angular velocity of the cylinder needs to be 0.6814 rad/s
The centripetal acceleration due to the rotation of the cylinder is given by the equation:
a = ω2r
Where a is the centripetal acceleration, ω is the angular velocity, and r is the radius of the cylinder. We can rearrange this equation to solve for ω:
ω = √(a/r)
Since we want the centripetal acceleration to be equal to the acceleration due to gravity on Earth, we can substitute in the appropriate values:
ω = √(9.8 m/s2/2.5 km)
ω = 0.6814 rad/s
What is centripetal acceleration?
Centripetal acceleration is the acceleration of an object moving in a curved path that is directed towards the center of the circle that it is moving in. It is caused by the force of the object's inertia, and is equal to the square of its velocity divided by the radius of the circle.
Therefore, The angular velocity of the cylinder needs to be 0.6814 rad/s
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Is a material made up of two or more substances that can be separated physically?
Yes, a mixture is a material made up of two or more substances that can be separated physically
A material that comprises one or more forms of the substance is referred to as a mixture. Either the element, the compounds, or both are to blame.
The term "mixture" refers to a situation in which two or more substances combine without engaging in a chemical reaction or other type of chemical transformation. The elements of have their original characteristics. The components of the combination can be separated. The mixture's component percentage is what determines the outcome. Examples of mixtures include cement, smog, ocean, ink, and air.
The two categories of mixtures are heterogeneous mixtures and homogeneous mixtures.
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To maintain a higher temperature (in a thermostat), which way should the control knob be moved?-to the right so that it moves towards the contacts, or to the left? Explain why?
Turn the dial either clockwise to make the unit colder or anticlockwise to make the unit warmer to set the thermostat to any temperature.
What is thermostat?A thermostat is a part of a regulating mechanism that senses the temperature of a physical system and takes action to keep it close to a desired setpoint.
Any system or gadget that heats or cools to a setpoint temperature uses a thermostat. Examples include central heating systems for buildings, air conditioners, HVAC systems, water heaters, kitchen appliances like refrigerators and ovens, and incubators for use in science and medicine.
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Whenever the net force on an object is zero, its acceleration: _________
Whenever the net force on an object is zero, its acceleration must be zero
Hence, option (a) is correct choice.
When we say a body is in motion, we imply that it changes its location in relation to some immovable object.
Newton's three laws of motion assist us in calculating the acceleration and force acting on the object.
Newton's First Law is a specific case of Newton's Second Law where F, the net force, is zero.
When this occurs, the acceleration must be 0 as well.
The velocity does not change since acceleration is defined as the change in velocity divided by the elapsed time.
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The missing option should be:
(a) zero
(b) One
(c) Infinity
(d) Undefined
If an astronaut weighs 130 lbs on Earth, would that astronaut weigh more or less on Jupiter? Explain your answer
Answer: The astronaut would weigh more on Jupiter than on Earth since Jupiter is several times bigger than Earth and therefore has a stronger gravitational pull, which weighs the astronaut down more.
Explanation: Jupiter's gravity is 2.4 times that of Earth
how to calculate per unit inventory value
To calculate per unit inventory value, divide the total value of the inventory by the number of units.
Per unit inventory value is a measure of the value of each individual unit in a company's inventory. To determine the per unit inventory value, the total value of the inventory is divided by the number of units. This calculation provides a snapshot of the average value of each unit in the inventory and can be used to make informed decisions about inventory management, such as determining when to sell items or when to order new units.
The per unit inventory value is an important metric for businesses as it helps them to understand the value of their assets and make decisions that maximize profitability and minimize waste.
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Which phenomenon is a result of the gravitational force of the Sun?
O rotation of the planets on their axes
O rotation of the Moon on its axis
O revolution of the Moon around Earth
O revolution of the planets around the Sun
Answer:
revolution of the planets around the Sun.
Explanation:
The revolution of the planets around the Sun is a result of the gravitational force exerted by the Sun. The Sun's gravitational pull attracts the planets, causing them to move in an elliptical orbit around it. This motion is known as the revolution of the planets around the Sun. The other options listed (rotation of the planets on their axes, rotation of the Moon on its axis, and revolution of the Moon around Earth) are also related to motion and gravity, but they are different phenomena.
If the test particle is replaced by a negatively charged test particle, is it in stable or unstable equilibrium at that location?
a) The test particle is in a stable equilibrium regardless of dimensionality.
b) The test particle is in stable equilibrium if these particles are constrained to one dimension and in unstable equilibrium if the particles can move in at least two dimensions.
c) The test particle is in stable equilibrium if these particles are constrained to one or two dimensions and in unstable equilibrium if the particles can move in three dimensions.
d) The test particle is in an unstable equilibrium regardless of dimensionality.
Option B. The behavior of a test particle in an electric field depends on its charge, the magnitude of the field, and the number of dimensions in which the particle can move.
In general, a negatively charged test particle placed in a uniform electric field will experience a force that is directed towards the positive electrode. If the particle is constrained to one dimension (e.g. it can only move along a straight line), it will be in stable equilibrium at the location where the net electric force on it is zero. In this case, any perturbation from that position will result in a restoring force that will bring the particle back to its original position.
However, if the particle is free to move in two or more dimensions, it will experience a net force in a direction other than the direction of the electric field. This means that the particle will be in an unstable equilibrium, as any perturbation from its position will result in a net force that will move the particle away from its original position, rather than back towards it.
In summary, the stability of the equilibrium depends on both the charge of the particle and the number of dimensions in which it can move. A negatively charged particle in a uniform electric field is in stable equilibrium if it is constrained to one dimension, and in unstable equilibrium if it can move in at least two dimensions.
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the 150 kg uniform crate rests om the 10 kg cart. determine the maximum force p that can be applied to the handle without causing the crate to tip on the cart. slipping does not occur.
The maximum force P that can be applied to the handle without causing the crate to tip on the cart is calculated to be 785 N.
It is given that the weight of the crate is 150 kg and weight of the cart is 10 kg.
The dimensions of the crate are given in the figure below.
The second figure in the attachment gives the free body diagram of the crate and the cart.
Tipping will occur about the edge A. Referring to the free body diagram and the kinetic diagram of the crate from figure(a), we can write,
ΣMa = (ΣMk)a
150 × 9.81 × 0.25 = (150a) 0.5
75 a = 367.875
a = 4.905 m/s²
Using the result of a and referring to the free body diagram of the crate and the cart in figure b,
Σ Fx = m (aG)x
P = (150 + 10) (4.905) = 784.5 N ≈ 785 N.
The given question is incomplete. The complete question has a figure attached in the attachment below.
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galileo classified qualities into primary and secondary. he thought the primary are quantifiable and real in the world and that secondary are not quantifiable and not real in the world. which are primary?
Galileo classifies qualities into primary and secondary qualities. Primary qualities are those that are inherent in an object and cannot be changed.
key characteristics include, An object's mass, which defines its weight and measures its resistance to acceleration, is the total amount of matter in the object.
The length, width, and height of an object establish its size or dimensions, which in turn determine its volume.
Shape: An object's form or configuration, which influences how it looks and how it is outlined.
Motion is the act of an item moving, including its speed, acceleration, and direction.
Location: An object's coordinates can be used to define its position in space.
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Two billiard balls collide. Identify the type of collision.
answer choices
O elastic
O nearly elastic
O inelastic
O perfectly inelastic
The collision type of two billiard balls collision is the Elastic collision.
An elastic collision is one in which the system does not experience a net loss of kinetic energy as a result of the collision. Two pool balls colliding and then moving independently is one example. A pair of identically sized pool balls are moving straight in the same direction at the same pace. They collide in a direct, elastic collision.
A collision that is fully elastic is one in which there is no kinetic energy lost during the contact. A collision is said to be inelastic if any of the kinetic energy is converted to another kind of energy during the impact.
The sort of collision that occurs when items don't cling together may be determined by calculating the start and end kinetic energies of the impact and comparing them. The collision is elastic if the kinetic energy is the same.
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(a) determine the polynomial that represents the total stopping distance t.
The polynomial is [tex]S = u \ t + \frac{1}{2} at^{2}[/tex]. It is also called second equation of motion.
The rate at which the speed and direction of a moving object vary over time is known as acceleration. When anything begins to move faster or slower, it is said to be accelerating. Because the direction is always changing, travel on a circle accelerates even while the speed is constant. All other motions are accelerated by both impacts. Due to the fact that it has both a magnitude and a direction, acceleration is a vector quantity. The definition of acceleration is the change in velocity vector during a period of time divided by the period of time.
[tex]S = u \ t + \frac{1}{2} at^{2}[/tex]
here
S= total stopping distance
u= initial velocity
a= acceleration
t= time taken to stop
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what is the magnitude of the force required to keep the rod moving at a constant speed?
The magnitude is 0.08N
i= e/R
= 0.8/(1)(30+30+20)×10^−2
=0.1A
F=iB=(0.1)(0.2)(4)=0.08N
What is magnitude?
The magnitude of a force refers to the sum of all forces acting on an object. If all forces act in the same direction, then the magnitude of the force increases. If forces act on an object in different directions, then the magnitude of the force decreases.To know more about magnitude, click the link given below:
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You are traveling on an interstate highway at the posted speed limit of 70 mph when you see that the traffic in front of you has stopped due to an accident up ahead. You step on your brakes to slow down as quickly as possible. Assume that you to slow down to 30 mph in about 5 seconds.
a) The magnitude of the average acceleration of the car while it is slowing down is 3.48 m/s².
b) With this same average acceleration, it would take 3,85 seconds longer to stop.
c) What total distance we would travel from when we first apply the brakes until the car stops is 140.76 m.
The problem is solved using the equations in uniformly accelerated straight motion.
Equations in Uniformly Accelerated Straight MotionThe equations apply in horizontal dimension are
v₁ = v₀ + at
v₁² = v₀² + 2ax
x = v₀t + ½ at²
Where
v₀ = initial velocityv₁ = final velocitya = accelerationt = timex = distanceWe are travelling on an interstate highway at a speed of 70 mph.
v₀ = 70 mphWe has to stop due to the accident up ahead so that we step on the brakes to slow down. We reach the speed of 30 mph in 5 seconds.
v₁ = 30 mpht₁ = 5 sConvert the unit of speed!
v₀ = 70 × 0.44704 m/s = 31.3 m/s
v₁ = 30 × 0.44704 m/s = 13.4 m/s
With that change in velocity, the average acceleration (deceleration) is
v₁ = v₀ + at₁
13.4 = 31.3 + a(5)
5a = 13.4 - 31.3
5a = - 17.9
a = - 3.58 m/s²
(Negative value indicates deceleration)
Now, use v₁ as initial speed. With the same acceleration, the additional time to stop will be
v₂ = v₁ + at₂
0 = 13.4 + (-3.48)t₂
13.4 = 3.48t₂
t₂ = 3,85 s
The total distance from stepping the brakes to stop will be
v₁² = v₀² + 2ax
0 = 31.3² + 2(-3.48)x
979.69 = 6.96x
x = 140.76 m
Your question is incomplete, but most probably your full question was
You are traveling on an interstate highway at the posted speed limit of 70 mph. When you see that the traffic in front of you has stopped due to an accident up ahead. You step on your brakes to slow down as quickly as possible. Assume that you to slow down to 30 mph in about 5 seconds.
a) What is the magnitude of the average acceleration of the car while it is slowing down?
b) With this same average acceleration, how much longer would it take you to stop?
c) What total distance would you travel from when you first apply the brakes until the car stops?
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in a double slit experiment, the slit separation is constructed to be exactly 12 times the wavelength of the light passing through the slits. at what angle from the center of the pattern will the third bright fringe occur?
Approximately 0.25 radians.
What is wavelength light?Wavelength light can be defined as the distance between the two successive crests or troughs of the light wave.
The angle of the third bright fringe in a double slit experiment can be calculated using the formula:
θ = sin^-1 (mλ/d)
where θ is the angle from the center of the pattern,
m is the order of the fringe (in this case, m = 3)
λ is the wavelength of the light and d is the separation between the slits.
Given that the slit separation is exactly 12 times the wavelength of the light we can substitute d = 12λ into the formula:
θ = sin^-1 (3λ/12λ)
θ = sin^-1 (1/4)
θ = approximately 0.25 radians.
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a load of 40 j 30 is connected to a source of 200 v with a phase angle of 30o, the total reactive power is:
A load of 40 j 30 is connected to a source of 200 v with a phase angle of 30o, The total reactive power is 640W.
We have given load ZL=40+j30
source voltage Vs= 200V
phase angle Ф= 30"
we have to calculate to total power delivered to load P.
so here circuit will be,
load Z - 40 +30
ZL=√(40) + (30)
ZL1600 900
ZL = √25,00
ZL = 50Ω
here angle cosΘ =R/Zl
by putting the values R=40 and Zl=50ohm
P=40*4*4=640W
A two-terminal device that can maintain a fixed voltage is a voltage source. An ideal voltage source can sustain the set voltage regardless of the output current or load resistance. The current that can be drawn from a voltage source in the real world is limited.
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two point charges are separated by a distance of 60.0 cm. the numerical value of one charge is twice that of the other. each charge exerts a force of magnitude 85.0 n on the other. 1) find the magnitude of the charge with a smaller magnitude. (express your answer to three significant figures.)
The magnitude of the smaller charge is 4.123106 × 10⁻⁵ C
What is charge ?
The physical quality of matter—its electric charge—is what causes it to feel a force when exposed to an electromagnetic field. Protons and electrons, the two types of charge carriers, typically carry positive and negative electric charges. Charges moving through a system produce energy.
What is magnitude ?
Magnitude in physics is simply described as "distance or quantity." It shows the size or direction that an object moves in either an absolute or relative sense. It is a way of expressing something's size or scope.
separation between the charges , r = 0.6 m
force exerted on each charge , f = 85 N
let the magnitude of the smaller charge be q
larger charge , Q = 2 * q
force , F = K * Q * q /r²
[tex]85=9\cdot 10^9\cdot 2\cdot \dfrac{q^2}{0.6^2}[/tex]
q = 4.123106 × 10⁻⁵ C
Thus, the magnitude of the smaller charge is 4.123106 × 10⁻⁵ C
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Which one has the LEAST acceleration?
a. An empty shopping cart pushed with a hard force
b. A full shopping cart pushed with a hard force
c. An empty shopping cart pushed with a light forces
d. A full shopping cart pushed with a light force
The option with the least acceleration is c. An empty shopping cart pushed with a light force.
Acceleration depends on the force applied and the mass of the object being pushed. An empty shopping cart has a lower mass than a full shopping cart, and a light force will result in a smaller acceleration than a hard force. Therefore, an empty shopping cart pushed with a light force will have the least acceleration.
A cyclist rides 6.31 km east, then 9.38 km in a direction 41.24 degrees west of north, then 7.53 km west. What is their displacement?
The displacement of the cyclist is 7.86 km at an angle of 45.03 degrees.
To find the displacement of the cyclist, we need to find the net change in position of the cyclist. We can break down the journey into three vectors: one for the eastward movement, one for the movement in the direction 41.24 degrees west of north, and one for the westward movement.
First, we can find the x- and y-components of the movement in the direction 41.24 degrees west of north using trigonometry:
x = 9.38 km * cos(41.24 degrees) = 7.54 km
y = 9.38 km * sin(41.24 degrees) = 5.21 km
Next, we can add the x-components and y-components of each of the three vectors to find the net change in x and y:
x = 6.31 km + 7.54 km - 7.53 km = 6.32 km
y = 5.21 km
Finally, we can find the displacement by finding the magnitude and angle of the vector (6.32 km, 5.21 km):
displacement = √(6.32 km)^2 + (5.21 km)^2 = 7.86 km
angle = atan(5.21 km / 6.32 km) = 45.03 degrees
So the displacement of the cyclist is 7.86 km at an angle of 45.03 degrees.
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Who identified the 5 elements of management?
Henry Mintzberg is credited with identifying the five elements of management.
Henry Mintzberg, a renowned Canadian management theorist and academic, is credited with identifying the five elements of management. In his book, "The Nature of Managerial Work," Mintzberg analyzed the work of managers and identified the five elements of management as: interpersonal, informational, decisional, and verbal and written communication.
The interpersonal element refers to the relationships between managers and other people, such as employees, customers, and suppliers. The informational element involves collecting, processing, and analyzing data to make informed decisions.
The decisional element refers to the role of managers in making decisions and solving problems. The verbal and written communication element includes the exchange of information and ideas through speaking, writing, and other forms of communication.
These five elements of management are considered key to understanding the work of managers and are widely used as a framework for analyzing and evaluating managerial work and activities.
However, it's important to note that the specific responsibilities and activities of managers can vary widely based on the size and type of organization, the industry, and the level of management.
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What is 28 degrees Celsius in Fahrenheit?
The formula for converting temperature, Celsius to Fahrenheit is °F = °C (9/5) + 32. As a result, 28° C is equivalent to 82.4° F.
What is temperature, exactly?
Like all other physical quantities, temperature is defined as the comparison of a substance's or object's warmth or coldness to some reference point. Even though it can be used to describe hot and cold circumstances, temperature is often measured using a thermometer with markings in several different temperature scales, the most popular of which are Celsius and Fahrenheit. There are numerous additional temperature units.
The SI Temperature Unit: What Is It?
The International System of Units (SI) uses the Kelvin (K) sign to denote the temperature unit. In science and engineering, the Kelvin scale is commonly acknowledged or utilised. In much of the world, temperature is typically expressed in degrees Celsius or Fahrenheit.
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to explain why he seems to hang in the air, calculate the ratio of the time he is above ymax/2 (moving up from ymax/2 to ymax and then moving down to ymax/2 ) to the time it takes him to go from the floor to that height. ignore air resistance.
The ratio of the time he is above ymax/2 (moving up from ymax/2 to ymax and then moving down to ymax/2 ) to the time it takes him to go from the floor to that height is 0.707 or 70%.
What is speed ?The rate of a directionally changing object's location. The SI unit of speed is created by combining the fundamental units of length and time. Meters per second (m/s) is the unit of speed in the metric system.
What is height ?From the highest point to the lowest, an entity's height would be measured. As a result, stating the vertical position and the distance from the minimum to maximum place or location are both necessary for measuring height. Height is the same as length in terms of dimensions.
[tex]$$Using equation 1 , we can write$$\begin{aligned}0= & u-g t_{\max } \\\text { or, } t_{\max } & =\frac{u}{g}\end{aligned}$$[/tex]
[tex]$$and applying equation 2, we get$$\begin{aligned}0^2 & =u^2-2 g y_{\max } \\\text { or, }^{y_{\max }} & =\frac{u^2}{2 g}\end{aligned}$$[/tex]
[tex]$$The time taken by the athelete to jump a height of $y_{\max } / 2$ is$$\begin{aligned}& \frac{y_{\max }}{2}=u t_{1 / 2}-\frac{1}{2} \times g t_{1 / 2}^2 \\& \text { or, } \frac{u^2}{4 g}=u t_{1 / 2}-\frac{g t_{1 / 2}^2}{2} \\\end{aligned}[/tex]
That is;
[tex]$$ \begin{aligned}& \text { or, } \frac{g}{2} \times t_{1 / 2}^2-u t_{1 / 2}+\frac{u^2}{4 g}=0 \\& \text { or, } t=\frac{u \pm \sqrt{u^2-u^2 / 2}}{2 \times g / 2} \\& \text { or, } t=\frac{u \pm 0.707 u}{g} \\& \text { or, } t=1.707 \times \frac{u}{g} \text { and } 0.293 \times \frac{u}{g} \\&\end{aligned}$$[/tex]
actually, the t= 1.707u/g is the time after which the athelete rich the height of ymax/2 in downward motion.
But when going upward, the atheletewill take 0.293u/g second to rech the height of ymax/2.
So, the time for which he was above ymax/2 is between 0.293 u/g to 1.707 u/g . i.e. the athelete will pend time above the height of ymax/2 for (1.707 -0.293) x u/g or 1.414 x u/g seconds seconds.
So, the ratio of the time he is above ymax /2 to the time it takes him to go from the floor to that height is
[tex]$ \text{ratio} = \frac{u/g}{1.414 \times u/g} = 0.707[/tex]
Thus, The ratio of the time he is above ymax/2 (moving up from ymax/2 to ymax and then moving down to ymax/2 ) to the time it takes him to go from the floor to that height is 0.707 or 70%.
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Complete question:
In the vertical jump, an athlete starts from crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00s in the air (thier "hang time"). Treat the athlete as a particle and let ymax be his maximum height above the floor. To explain why he seems to hang in the air, calculate the ratio of the time he is above ymax /2 to the time it takes him to go from the floor to that height. You may ignore air resistance.
Points a and b lie in a region where the y-component of the electric field is Ey=α+β/y2. The constants in this expression have the values α = 600 N/C and β = 5. 00 N⋅m2/C. Points a and b are on the y-axis. .
Point a is at y = 2. 00 cm and point b is at y = 3. 00 cm. What is the potential difference Va−Vb between these two points. ?
The potential difference Va−Vb is 599.8233 N/C.
The potential difference between points a and b can be found using the expression for the electric potential difference, which is given by
Va - Vb = ∫(Ey)dy
where the integral is taken from y = 2 cm to y = 3 cm.
Substituting the expression for Ey, we get:
Va - Vb = ∫(α + β/y2)dy
= α(y) + β ∫(1/y2)dy
= α(3) - α(2) + β [−1/y] from y = 2 to y = 3
= 600 N/C * (3 - 2) + 5.00 N⋅m2/C * [-1/3 + 1/2]
= 600 N/C * 1 - 0.1767 N/C
= 600 - 0.1767
= 599.8233 N/C
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what is the average velocity between the times 0.4 s and 1 s?
The displacement divided by the time interval gives the average velocity, which is between 0.4 and 1s. The average velocity is 3 m/s as the distance between 0.4 and 1 seconds is 2m.
Given initial time (t1) = 0.4s
The final time (t2) = 1s
Displacement between the time interval (d) = 2m
The velocity of an object is the rate at which its position changes with respect to time. Due to the fact that it is a vector quantity, it possesses both magnitude and direction.
So, average velocity = total displacement/ time taken to travel
Then, v = 2/(1 - 0.4) = 2/0.6 = 3.33m/s
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A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled 7.80 m to the bottom of the incline is 3.80 m/s. What is the speed of the block when it is 4.80 m from the top of the incline?
The speed of the block when it is 4.80 m from the top of the incline is approximately 2.52 m/s.
We can use kinematic equations to determine the speed of the block at different points along the incline. The acceleration of the block can be determined from the equation: [tex]a = (vf^2 - vi^2)/2d[/tex], where vf is the final velocity, vi is the initial velocity (0 m/s in this case), and d is the distance traveled. Plugging in the given values, we find that
[tex]a = (3.80 m/s)^2/2(7.80 m) = 0.97 m/s^2.[/tex]
Next, we can use the equation vf = vi + at to determine the velocity of the block at a given point along the incline. Plugging in
t = [tex](4.80 m)/(0.97 m/s^2)[/tex] = 4.94 s, we find that
vf = 0 m/s + 0.97 [tex]m/s^2[/tex] x 4.94 s = 4.80 m/s = 2.52 m/s.
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