Answers
Answer:
0.65 m/s NORTH
Explanation:
North is +, south is -
let V = velocity of the 0.12 kg ball AFTER the collision
Law of conservation of momentum (P = mv) states that total momentum before the collision must equal total momentum after the collision.
(0.10 kg)(9.6 m/s) - (0.12 kg)(7.6 m/s) = -(0.10 kg)(0.30 m/s) + (0.12 kg)(V)
Before → After
0.96 kg·m/s - 0.912 kg·m/s = -0.03 kg·m/s + 0.12 kg(V)
0.048 kg·m/s + 0.03 kg·m/s = 0.12 kg(V)
0.078 kg·m/s = ·0.12 kg(V)
V = 0.078 kg·m/s / 0.12 kg = 0.65 m/s NORTH
Related Questions
How does understanding the formation of the sun contribute to understnading how it releases electromagnetic energy, including sunlight, which allows Earth to be what it is today?
Answers
Radiant energy that moves in waves at the speed of light is known as electromagnetic energy. Radiant energy, electromagnetic radiation, electromagnetic waves, light, or the movement of radiation are other names for it.
What is Electromagnetic waves?James Clerk Maxwell, a 19th-century physicist whose research had a major impact on the development of quantum mechanics, discovered electromagnetic radiation.
We can think of electromagnetic energy or radiation functioning similarly to a typical ocean wave in terms of how it operates. The radiation is the water in this analogy.
Radiation from an electromagnetic field can transfer heat. Heat, energy, or light waves are transmitted from one place to another across a vacuum or a medium using electromagnetic waves.
Therefore, Radiant energy that moves in waves at the speed of light is known as electromagnetic energy. Radiant energy, electromagnetic radiation, electromagnetic waves, light, or the movement of radiation are other names for it.
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How much does a spring with a spring constant of 650 N/m need to be compressed in order to store 20.0 J of elastic potential energy?
Answers
The spring needs to be compressed by 0.175 meters in order to store 20.0 J of elastic potential energy.
What is elastic potential energy?Elastic potential energy is the energy stored in an object when it is deformed or stretched due to an applied force. It is present in springs, rubber bands, and other elastic materials that can be stretched and then return to their original shape.
The amount of elastic potential energy stored in an object is directly proportional to the amount it is stretched or compressed, and is proportional to the square of the deformation. The formula for elastic potential energy is given by U = (1/2)kΔx^2, where U is the elastic potential energy, k is the spring constant, and Δx is the change in length of the object. When the force is removed, the stored elastic potential energy is converted into kinetic energy, causing the object to return to its original shape.
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Understanding Motion from a graph An object is moving along a straight line. The graph shows the object's velocity vs. time. During which interval(s) of the graph does the speed of the object increase by equal amount in equal times? 2s to 3 s 3s to 5s 0 s to 2 s and 3 s to 5 s 0 to 2 s, and 5 to 6 s
Answers
The time that the speed of the object increase by equal amount in equal times is 0 s to 2 s .
What is uniform acceleration?Uniform acceleration is a type of acceleration in which an object moves in a straight line and the magnitude of its acceleration remains constant over time. In other words, the object's velocity increases by an equal amount in equal time intervals.
In the case of uniform acceleration, the velocity of an object changes at a constant rate, making it a key concept in kinematics and the study of motion.
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A student was riding his bicycle from north to south at a speed of 5 m/s when it started to rain. If the rain was falling vertically downward with a
velocity of 10 m/s, in which direction should he hold his umbrella?
Answers
Answer:
The student should hold his umbrella at an angle facing south-west.
A hot-air balloonist, rising vertically with a constant velocity of magnitude v=5.00 m/s, releases a sandbag at an instant when the balloon is a height h=40.0m above the ground (Figure 1). After it is released, the sandbag is in free fall. For the questions that follow, take the origin of the coordinate system used for measuring displacements to be at the ground, and upward displacements to be positive.
A) Compute the position of the sandbag at a time 0.245 s after its release.
B) Compute the magnitude of the velocity of the sandbag at a time 0.245s after its release.
C) Determine the direction of the velocity of the sandbag at a time 0.245 s after its release.
D) Compute the position of the sandbag at a time 1.15 s after its release.
E) Compute the magnitude of the velocity of the sandbag at a time 1.15 s after its release.
F) Determine the direction of the velocity of the sandbag at a time 1.15 s after its release.
Answers
a. The position of the sandbag at a time 0.245 s after its release is 39.706 m from the ground.
b. The magnitude of the velocity of the sandbag at a time 0.245 s after its release is 2.4 m/s.
c. The direction of the velocity of the sandbag at a time 0.245 s after its release is to the ground.
d. The position of the sandbag at a time 1.15 s after its release is 33.52 m from the ground.
e. The magnitude of the velocity of the sandbag at a time 1.15 s after its release is 11.27 m/s.
f. The direction of the velocity of the sandbag at a time 1.15 s after its release is to the ground.
According to the free-fall motion, when an object is released without an initial velocity from a certain height the object will experience acceleration due to the gravitational force of the earth. The non-uniform motion formula
v = u + at
d = (u × t) + 0.5at²
u = initial velocity = 0t = time (s)a = accelerationg = acceleration due to gravity
a = g = - 9.8 m/s²
Negative because moves downward
The formula for free-fall motion become
v = u + at ⇒ v = gt
d = (u × t) + 0.5at² ⇒ d = 0.5gt²
When the sandbag is released by the balloon at h = 40.0 m, it moves in a free-fall motion.
At t = 0.245 s
The sandbag traveledd = 0.5gt² = 0.5 × - 9.8 × 0.245² = - 4.9 × 0.060025
d = - 0.294 mThe position
h + d = 40.0 - 0.294 m = 39.706 m from groundThe velocity
v = gt = - 9.8 × 0.245
v = - 2.401 m/s
v = - 2.4 m/s
with direction to the ground
At t = 1.15 s
The sandbag traveledd = 0.5gt² = 0.5 × - 9.8 × 1.15² = - 4.9 × 1.3225
d = - 6.48 mThe position
h + d = 40.0 - 6.48 m = 33.52 m from groundThe velocity
v = gt = - 9.8 × 1.15
v = - 11.27 m/s
with direction to the ground
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The lowest pressure ever obtained in a laboratory setting is 4.0×10−11 Pa. At this pressure, how many molecules of air would there be in a 50 Celsius experimental chamber with a volume of 0.060 m3?
Answers
There would be 5.38 × 10¹⁹ number of molecules of air at that condition.
What is ideal gas?A theoretical gas known as an ideal gas is made up of several randomly moving point particles with no interparticle interactions.
Because it abides by the ideal gas law, a condensed equation of state, and is amenable to statistical mechanics analysis, the ideal gas concept is helpful.
The amount of air = PV/RT
= (4.0 × 10 ⁻¹¹× 0.060)/ 8.314 ×(273 + 50) mole
= 8.93714 × 10⁻⁵ moles.
molecules of air would there be = 8.93714 v × 6.023 × 10²³ = 5.38 × 10¹⁹
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A robot is being built using two 12 Volt batteries connected in series. What resistance should be used in the circuit if the motors need 2.5 Amps to work correctly?
Answers
The static values of circuit components, current rates, voltage sources, and voltage drops can all be verified using Ohm's Law.
What is Ohm's law?A test instrument may indicate that resistance has dropped or voltage has increased, resulting in a high-voltage condition, if it detects, for instance, a higher than usual current reading. This can point to a supply or circuit problem.
A lower than usual current reading in a direct current (dc) circuit could indicate that the voltage has dropped or the circuit resistance has risen. Poor or loose connections, corrosion, and/or broken components are potential sources of higher resistance.
Electrical current is drawn by the loads of a circuit. Any type of component, including small electrical gadgets, computers, home appliances, or a sizable engine, can be a load.
Therefore, The static values of circuit components, current rates, voltage sources, and voltage drops can all be verified using Ohm's Law.
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change the speed0.200cm/s to km/yr
Answers
When we change the speed 0.200cm/s to km/yr we get 6.5 × 10⁴ km/yr.
What is Speed?
Speed refers to the rate at which something moves or operates, usually measured in units of distance per time, such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph). In physics, speed is defined as the magnitude of velocity, which is a vector quantity that describes the rate of change of an object's position. Speed is often used in many areas, such as transportation, sports, and technology.
We know that
1km = 1000m
1m = 100cm
and
1 year = 365day
1 day = 24 hours
1 hour - 60 min
1 min = 60 sec
With this, we have
[tex]$ \frac{200 \text{cm}}{1 \text{sec}} = \frac{200 \times 100\text{cm} \times 1000 \text{cm}}{60\ \text{sec}\times 60\ \text{sec}\times 24 \text{hours} \times 356 \text{days}}[/tex]
0.00065 km/yr
Thus, When we change the speed 0.200cm/s to km/yr we get 6.5 × 10⁴ km/yr.
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Use the following information to answer questions 2-4. Two people are playing a game of
tug-of-war with the rope attached to a mass of 25 kg at the center. The person pulling to
the left pulls with a force of 20 N. The person pulling to the right pulls with a force of 10 N.
2. Which direction will the 25 kg mass move?
a. Left
b. Right
C. It will not move
How do you know?
What will the velocity of the mass be after 1 second?
What will the velocity of the mass be after 2 seconds?
Answers
The direction in which the 25 kg mass will move is to the Left. The correct option is A.
This is because the force pulling to the left is greater than that to the right.
The velocity of the mass after 1 second will be 0.4 m/s
The velocity of the mass after 2 seconds will be 0.8 m/s
What is the net force on the mass of 25 kg?The net force o the mass of 25 kg is given below:
Net force = 20 N - 10 N
Net force = 10 N
The velocity of the mass is given by the formula below:
Velocity = net force * time / mass
velocity after 1 second = 10 * 1 / 25
velocity after 1 second = 0.4 m/s
velocity after 2 seconds = 10 * 2 / 25
velocity after 2 seconds = 0.8 m/s
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The Boring Company has proposed transporting people between Los Angeles and San Francisco, a distance of 540 km, through an underground tube from which the air has been removed to eliminate air drag. Small pods carrying four passengers would accelerate at 2.5 m/s2 until reaching a speed of 330 m/s. Later they would brake at 1.5 m/s2. A launch of one pod per minute would transport 240 passengers per hour, roughly equivalent to one jet plane per hour.
A)What would be the trip time in minutes from Los Angeles to San Francisco?
B)How far apart would two adjacent pods be on the constant-speed segment of the journey?
Answers
A launch of one pod per minute would transport 240 passengers per hour, roughly equivalent to one jet plane per hour. The total speed is 235 km/s2.
What is acceleration?acceleration, rate at which velocity changes with time, in terms of both speed and direction. A point or an object moving in a straight line is accelerated if it speeds up or slows down.
Motion on a circle is accelerated even if the speed is constant, because the direction is continually changing. For all other kinds of motion, both effects contribute to the acceleration.
Because acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is also a vector quantity. Acceleration is defined as the change in the velocity vector in a time interval, divided by the time interval.
Therefore, A launch of one pod per minute would transport 240 passengers per hour, roughly equivalent to one jet plane per hour. The total speed is 235 km/s2.
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how much energy must be absorbed by 20 point grams of water to increase its temperature from 283 degrees Celsius to 303°C 
Answers
The amount of energy required to increase the temperature of 20 g of water from 283°C to 303°C is approximately 6.1 kJ.
How much energy must be absorbed by 20 point grams of water to increase its temperature from 283 degrees Celsius to 303°C?To calculate the amount of energy absorbed by 20g of water when its temperature increases from 283°C to 303°C, you must use the formula for specific heat capacity.Specific heat capacity is the amount of energy required to raise the temperature of 1g of a substance by 1°C. The formula for specific heat capacity is Q=mcΔT, where Q is the energy absorbed, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature. In this case, the mass of the water is 20g, the change in temperature is 20°C, and the specific heat capacity of water is 4.2 J/g°C. Therefore, the energy required to increase the temperature of 20g of water from 283°C to 303°C can be calculated as follows: Q= 20g x 4.2 J/g°C x 20°C = 1680J. Therefore, the amount of energy absorbed by 20g of water to increase its temperature from 283°C to 303°C is 1680J.
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Starting from a location with position vector 1,=−18.7 m
and 1,=21.5 m
, a rabbit hops around for 10.7
seconds with average velocity ,=−2.17 m/s
and ,=1.71 m/s
. Find the components of the position vector of the rabbit's final location, 2,
and 2,
^ is the same as the picture
Answers
The components of the position vector of the rabbit's final location r₂, x and r₂, y is 36.77 m.
How to calculate position?To find the final location of the rabbit, calculate the displacement of the rabbit, which is given by the product of average velocity and time.
r₂, x = 1, + vx x t = -18.7 - 2.17 x 10.7 = -43.77 m
r₂, y = 1, + vy x t = 21.5 + 1.71 x 10.7 = 36.77 m
Therefore, the components of the position vector of the rabbit's final location are r2x = -43.77 m and r2y = 36.77 m.
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a piece of uranium drops from 1500 Celsius to 900 Celsius. what state of matter would we expect it to be in?
Answers
At 1500°C, uranium would be in a molten or liquid state. As it cools to 900°C, it will solidify
How does the temperature affect?
The temperature of a substance determines its state of matter. At high temperatures, substances tend to be in a liquid or gaseous state, and as the temperature decreases, they solidify.
In the case of uranium, at 1500°C, it would be in a molten or liquid state because this temperature is higher than its melting point of 1132°C.
However, as it cools to 900°C, it will become solid because 900°C is below its melting point.
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draw the output voltage of point A of the given circuits
Answers
For full negative cycle and some part of positive cycle, there is be a voltage drop across the load.
What is diode?A diode is a semiconductor gadget that essentially switches current in a single direction. While significantly limiting current flow in the opposite direction, it permits easy flow in one direction.
In this given circuit, diode is placed such that the only positive half cycle of ac voltage can passes through it but an opposite potential also applied. Hence, for a certain level and upward the diode acts as short and for full negative cycle and some part of positive cycle, there is be a voltage drop across the load.
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Two cars A and B are moving at speeds of 60 km/h and 80km/h respectively .what is the speed of car A relative to car B if the two cars are moving on the same direction
Answers
Answer:
A
Explanation:
A very thin sheet of brass contains two thin parallel slits. When a laser beam shines on these slits at normal incidence and room temperature (20.0 ∘C ), the first interference dark fringes occur at ± 26.6∘ from the original direction of the laser beam when viewed from some distance. If this sheet is now slowly heated up to 135 ∘C , by how many degrees do these dark fringes change position? Coefficient of linear expansion for brass is α=2.0×10−5(∘C)−1 . Ignore any effects that might occur due to change in the thickness of the slits. (Hint: Since thermal expansion normally produces very small changes in length, you can use differentials to find the change in the angle.)
Answers
We do not know the value of L0 and d, we cannot calculate the exact change in angle. However, we can find the order of magnitude of Δθ by using the values given in the problem.
How solve the problem?The change in the angle can be calculated by using the formula for linear expansion: ΔL = L0 * α * ΔT, where ΔL is the change in length, L0 is the initial length, α is the coefficient of linear expansion, and ΔT is the change in temperature.
We can assume that the distance between the two slits is the length L0. The change in length ΔL will cause a change in the angle of the dark fringes, which can be calculated using the formula: Δθ = ΔL / d, where Δθ is the change in angle and d is the distance from the slits to the observation point.
So, ΔL = L0 * α * ΔT = L0 * α * (135 - 20)
Δθ = ΔL / d
Substituting the given values, we get:
Δθ = L0 * α * (135 - 20) / d
= L0 * 2.0 x 10^-5 * 115 / d
Since we do not know the value of L0 and d, we cannot calculate the exact change in angle. However, we can find the order of magnitude of Δθ by using the values given in the problem.
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need help with # 5,6,&7 please, thanks
Answers
Answer: 5. 1/2 fraction of a wave comes by each second. 6. 1/10 of the wave comes by each second 7. 3.
Explanation: 5. The formula for frequency is f = 1/t, T being period, so the frequency is 1/2.
Same thing with the 6th question, f=1/10
The 7th question asks about celerity, the wave celerity is the speed c at which the wave moves in the x-direction, is given by c=L/T, with L being the wavelength and T being the period.
Therefore C= 6/3, C= 3.
Why did Khan change 1 minute to seconds while finding the displacement of Marcia if she travels at a velocity of 5 meters per second south for 1 minute?
Answers
Answer:fdxv
Explanation:
fdc
A piece of lithium goes from 65 Celsius to 200 Celsius what state of matter would be expected to be in 
Answers
At 65°C, lithium is a solid. At 200°C, liquid would be the state of matter.
What is state of matter?State of matter refers to the physical form in which a substance exists. There are four main states of matter: solid, liquid, gas, and plasma. In a solid, particles are closely packed together and have a fixed shape and volume. In a liquid, particles are close together but can flow and take the shape of their container. In a gas, particles are widely spread out and have a much larger volume and take the shape and volume of their container. In plasma, particles are highly ionized and have unique electrical and thermal properties.
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Please answer this question
Answers
A mechatronic system can be a common household appliance such as a washing machine, a car engine, or an industrial production line.
Using the parts above, what is the washing machine component?For example, in a washing machine, the actuators could be the DC motors that control the drum's rotation, the solenoids that control water flow, and the voice coils that control the drum's position.
The sensors could be switches that detect the lid's position, the photoelectrics that detect the presence of clothes, and the potentiometers that measure the drum's position.
The input signal conditioning and interfacing could be the discrete circuits that filter and amplify the signals from the sensors.
The graphical displays could be the LED lights that indicate the status of the machine, and the output signal conditioning and interfacing could be the amplifiers and power transistors that control the actuators.
The digital control architecture could be the microcontroller that implements the control algorithms and sequences the operations of the machine.
This is just an example of how to map a mechatronic system, and the components and their arrangement can vary greatly depending on the specific system being analyzed.
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A bird is flying due east. Its distance from a tall building is given by x(t)=29.0m+(12.8m/s)t−(0.0450m/s3)t3. What is the instantaneous velocity of the bird when t = 8.0s?
Answers
The velocity of the bird would be 4.16 m/s².
What is instantaneous velocity?The velocity of a body at any specific instant of time is called instantaneous velocity. Mathematically, we can write -{v} = dx/dt
Given is that a bird is flying due east. Its distance from a tall building is given by -
x{t} = 29 + 12.8t - 0.0450t³
Instantaneous velocity is given by -
{v} = dx/dt ... Eq { 1 }
Now -
v = dx/dt = d/dt (29 + 12.8t - 0.0450t³)
v = dx/dt = 0 + 12.8 - (3 x 0.0450t²)
v = dx/dt = 12.8 - 0.135t²
v{8} = dx/dt = 12.8 - 0.135 x 8 x 8
v{8} = dx/dt = 12.8 - 8.64
v{8} = dx/dt = 4.16
Therefore, the velocity of the bird would be 4.16 m/s².
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You weigh 730 N.
What would you weigh if the Earth were
two times as massive as it is and its radius
were two times its present value?
Answer in units of N. Answer in units of
N.
Answers
Light travels 186,282 miles per second.How far does it travel in an hour? IN A DAY?
Answers
A. Light travels approximately 670,616,320 miles in an hour.
B. Light travels approximately 16,094,718,080 miles in a day.
How to find out how far it travels in an hour ?Light travels at a speed of 186,282 miles per second. To find out how far it travels in an hour, we can simply multiply this speed by the number of seconds in an hour:
Distance traveled in an hour = 186,282 miles/second x 3,600 seconds/hour = 670,616,320 miles/hour
Therefore, light travels approximately 670,616,320 miles in an hour.
How to find out how far light travels in a day?To find out how far light travels in a day, we need to multiply the distance traveled in an hour by the number of hours in a day:
Distance traveled in a day = 670,616,320 miles/hour x 24 hours/day = 16,094,718,080 miles/day
Therefore, light travels approximately 16,094,718,080 miles in a day.
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During a typical afternoon thunderstorm in the summer, an area of 57.0 km2 receives 5.81 X 10^8 gal of rain in 18 min. How many inches of rain fell during this 18 min period?
Answers
1.5189 inches of rain fell during this 18 min period.
What is the unit of rainfall?The amount of rain that fell in total over a specific time period, measured in millimeters, is the most typical rainfall measurement.
Area = 57.0 km² = 57.0 × 1000 × 1000 m²
Volume of water = 5.81 × 10⁸ gallon = 5.81 × 10⁸ × 0.00378541 m³ = 2199323.21 m³
Hence, the height of the rain water
= (2199323.21 m³) ÷ (57.0 × 1000 × 1000 m²)
= 0.03858 m
= 0.03858 × 39.3701 inch
= 1.5189 inch
So, 1.5189 inches of rain fell during this 18 min period.
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A sprinter with a mass of 70 kg accelerates at a rate of 5 m/s2. What force is the sprinter exerting?
Answers
Answer:
The force exerted by the sprinter can be calculated using Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
F = m * a
where:
F is the force
m is the mass of the object (70 kg)
a is the acceleration (5 m/s^2)
Plugging in the values, we get:
F = 70 kg * 5 m/s^2
F = 350 N
So, the sprinter is exerting a force of 350 N. This is the force that the sprinter's legs are applying to the ground, propelling them forward and producing the acceleration.
A bullet is fired upward with a speed v0 from the edge of a cliff of height h
a. What is the speed of the bullet when it passes by the cliff on its way down?
b. What is the speed of the bullet just before it strikes the ground?
c. If the bullet is instead fired downward with the same initial speed v0, what is its speed just before it strikes the ground?
Express your answers in terms of v0, h and g. Ignore air drag. Assume the bullet is fired straight up in (a) and (b) and straight down in (c).
Answers
The speed of the bullet when it passes by the cliff on its way is V0 itself which is equal to h/t. The speed just before it strikes the grounds will be √2gh.
What is speed ?Speed is a physical quantity measuring the distance travelled per unit time. It depends on the mass of the object as well some external factors such as friction, air resistance etc.
Here, the initial velocity of the bullet = V0
the speed of the bullet within a time t to pas the height of the cliff will be h/t.
Now, the kinetic energy of the ball just before it striking the ground is equal to its potential energy.
hence, 1/2 mv² = mgh
then v = √2gh.
If the bullet is instead fired downward with the same initial speed v0, then it is accelerating downwards then the speed is √2gh + V0.
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A displacement-time graph is drawn below.
Displacement (m)
80
5
12
20 Time (s)
Find the displacement for the whole journey.
Answers
The total displacement of the journey is 80 m.
What is the displacement?Displacement is a vector quantity that describes the change in position of an object from its initial position to its final position in a given reference frame.
It is equal to the difference between the final position and the initial position of an object and is commonly used in physics and engineering to describe motion. Displacement is usually measured in units of length such as meters.
The graph can show us the that point of the highest displacement is 80m.
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A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 2.0 m/s, skates by with the puck. After 1.80 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.32 m/s2, determine each of the following. (a) How long does it take him to catch his opponent? (Assume the player with the puck remains in motion at constant speed.) s (b) How far has he traveled in that time? mA hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 2.0 m/s, skates by with the puck. After 1.80 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.32 m/s2, determine each of the following. (a) How long does it take him to catch his opponent? (Assume the player with the puck remains in motion at constant speed.) s (b) How far has he traveled in that time? m
Answers
a. Time that the first player took to catch his opponent is 14.1 s after he makes up his mind to chase his opponent.
b. The player has traveled 31.8 m to catch his opponent.
According to uniform motion remains the same and the distance will increase with time. The formula to calculate distance
d = v × t
v = uniform speed (m/s)v = 2.0 m/st = traveled time (s)d = distance (m)
According to non-uniform motion, the speed will increase with time when the object has acceleration. The formula to calculate distance
d = (v₁ × t) + (0.5 × a ×t²)
v₁ = initial speed (m/s)v₁ = 0t = time (s)a = acceleration
a = 0.32 m/s²d = distance (m)
Two players didn't move at the same time. The second player moves first. After 1.80 s the first player just move.
Time traveled for the first player = tTime traveled for the second player = t + 1.80 sWhen the first player catches his opponent, the distance between the two is the same.
d first player = d second player
(v₁ × t) + (0.5 × a × t²) = v × t
(0 × t) + (0.5 × 0.32 × t²) = 2.0 × (t + 1.80)
0 + 0.16t² = 2.0t + 3.60
0.16t² - 2.0t - 3.60 = 0
multiply by 100
16.0t² - 200.0 - 360.0 = 0
divided by 8
2.0t² - 25.0t - 45.0 = 0
Using quadratic formula
a = 2.0b = - 25.0c = - 45.0t₁₂ = (- b ± (√(b² - 4ac))) ÷ 2at₁₂ = (25.0 ± (√((- 25.0)² - (4 × 2.0 × - 45.0)))) ÷ (2 × 2.0)
t₁₂ = (25.0 ± (√(625.0 + 360.0)) ÷ 4.0
t₁₂ = (25.0 ± (√985) ÷ 4
t₁₂ = (25.0 ± 31.38) ÷ 4t₁ = (25.0 - 31.38) ÷ 4 = - 6.38 ÷ 4 = - 1.6 s impossiblet₂ = (25.0 + 31.38) ÷ 4 = 56.38 ÷ 4 = 14.1 sThe first player will catch after 14.1 s he moves.
The distance
d = (v₁ × t) + (0.5 × a × t²)
d = (0 × 14.1) + (0.5 × 0.32 × 14.1²)
d = 0 + (0.16 × 198.81)
d = 31.8 m
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An orange of mass 125 g falls from a branch to the ground 3.50 m below. (a) Relative to the ground, what is the gravitational potential energy of the orange on the branch? On the ground? (b) Relative to the branch, what is the gravitational potential energy of the orange on the branch? On the ground? J (c) During the orange's fall, what is its change in gravitational potential energy relative to the ground? Relative to the branch?
Answers
(a) Relative to the ground, the gravitational potential energy of the orange on the branch is 4.29 J and on ground is 0 J.
(b) ) Relative to the branch, the gravitational potential energy of the orange on the branch is 0 J and on ground is 4.29 J.
(c) The change in potential energy relative to the ground is -4.29 J and relative to the branch is 0 J.
What is the gravitational potential energy?Relative to the ground, the gravitational potential energy of the orange on the branch is calculated as follows;
P.E = mgh
where;
m is the mass of the orangeh is the height of the branch above the groundg is acceleration due to gravityP.E = 0.125 kg x 9.8 m/s² x 3.5
P.E = 4.29 J
The gravitational potential energy of the orange on the ground is calculated as follows;
P.E = mgh
P.E = m x g x 0 m
P.E = 0 J
The change in potential energy = final potential energy - initial potential energy
change in potential energy relative to ground = 0 J - 4.29 J = - 4.29 J
change in potential energy relative to branch = 4.29 J - 4.29 J = 0
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I want you to tell me the difference between a Type I and a Type II error. Define each error (you can use the book's words if you like). Tell me in your own words what a Type I error is, using an example if that would help. Do the same for a Type II error. Why are Type I and Type II errors so harmful to research? Read your answer to someone else: if they don't get it, I won't, either. Be clear.
Answers
A Type I error, also known as a false positive, occurs when a statistical hypothesis test rejects a null hypothesis that is actually true. For example, consider a medical test for a certain disease.
What is a Type II error?A Type II error, also known as a false negative, occurs when a statistical hypothesis test fails to reject a null hypothesis that is actually false. In the medical test example, a Type II error would occur if the test result suggests that the person is healthy when they actually have the disease.
Both Type I and Type II errors are harmful to research because they can lead to incorrect conclusions and decision-making.
A Type I error can result in unnecessary treatments or actions, while a Type II error can result in missed opportunities to identify and address a problem. These errors can negatively impact the validity of research and its real-world applications.
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