Tiger Woods hits a golf ball off the edge of a 50 m high cliff, at an initial speed of 30 m/s and an initial angle = 40° from the horizontal. Neglect air resistance.
a) How long is the ball in flight?
b) How far from the base of the cliff does it land?
c) What is the ball's speed just before it hits the ground?

The spring exerts the same force on both glider A and glider B, equal to (Fa - (-6N))/2 = (Fb - (6N))/2.

The force of the spring can be calculated using Hooke's law, which states that the force exerted by a spring is proportional to the displacement of the spring from its rest position.

Let's call the spring force "Fspring". Since the spring is compressed, it is exerting a force on both gliders, which we can call "Fa" for glider A and "Fb" for glider B.

The total force on each glider is equal to the spring force plus the force of the 6N external force:

Fa = Fspring + (-6N)

Fb = Fspring + (6N)

Since the forces on both gliders are equal in magnitude and opposite in direction, we can write the following equation:

Fspring = (Fa - (-6N))/2 = (Fb - (6N))/2

To calculate the spring force, we need to find the displacement of the spring from its rest position. This can be done using the following equation:

Fspring = kx

Where;

k is the spring constant

Since the spring is compressed, the displacement "x" is negative. We can find the spring constant "k" using the equation:

k = Fspring / x

We can substitute the equation for Fspring from above into this equation:

k = (Fa - (-6N))/2x / x

We can rearrange this equation to solve for "x":

x = (Fa - (-6N))/(2k)

We can then substitute this value of "x" back into the equation for Fspring to find the force exerted by the spring:

Fspring = (Fa - (-6N))/2 = (Fb - (6N))/2

Since the masses of glider A and glider B are known, we can use the following equation to find the acceleration of each glider:

Fa = ma

Fb = mb

Where "m" is the mass of each glider and "a" is the acceleration of each glider.

We can rearrange these equations to solve for the acceleration of each glider:

a = Fa / m

b = Fb / m

Now that we have the acceleration of each glider, we can use Newton's second law to find the force exerted by the spring on each glider:

Fa = ma = 400 g * a

Fb = mb = 600 g * b

Finally, we can substitute the value of Fspring from above into these equations to find the force exerted by the spring on each glider:

Fa = Fspring + (-6N) = (Fa - (-6N))/2 + (-6N)

Fb = Fspring + (6N) = (Fb - (6N))/2 + (6N)

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To determine the effect of the temperature dependence of the thermal conductivity on the temperature distribution in a solid, consider a material for which this dependence may be represented as K=K1+aT.

Temperature and conductivity is inversely related as temeprature increases ,thermal diffusivity and thermal conductivity decrease. Thermal conductivity is related linearly so it  decrease with increasing temperature. At high temperature, thermal diffusivity and conductivity approach constant.

Given that

k = ko + aT

From Fourier law

Heat transfer per unit volume given as

x measured from left hand side of wall.

By integrating

qdx=-(ko + aT)dT

When a = 0 :

qx=-koT+C

This is become straight line.

When a > 0  :

dT/dX= increase

K decrease when x is increases.

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The required speed of the cat when the relative speed and the speed of the dog are given is calculated to be 8.25 m/s.

Distance by which the dog lags behind the cat is given as d = 4.2 m

Speed of the dog v₂ = 9 m/s

The dog catches the cat in time t = 5.6 s

Relative speed of the dog with respect to the cat is given by,

vr = v₂ - v₁ = 9 - v₁

where,

v₁ is the speed of the cat

Therefore, we can write,  

t = d/(9 - v₁)

Making v₁ as subject, we have,

v₁ = v₂ - d/t = 9 - 4.2/5.6 = 9 - 0.75 = 8.25 m/s

Thus, the speed of the cat is calculated to be 8.25 m/s.

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The gravitational force between the objects depends on their mass as well as distance between them. If the distance increases, the gravitational force decreases. Hence, the statement is false.

The gravitational force is the force by which an object attracts other object into its center of mass. The gravitational force depends on the masses of the objects and distance between them by the equation written below:

Fg = G m1 m2/r²

where G is the universal gravitational constant equal to 6.67 × 10⁻¹¹ N/kg²m²

As per this universal equation for gravitation, as the mass increases, gravitational force between the objects increases. If the force between the two masses decreases 2 times with an increase in distance.

Therefore, the statement is false.

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Answer:

ETo calculate the duration of the hammer's collision with the nail, we need to find the time it takes for the hammer to come to a stop and then reverse direction.

The hammer's initial momentum before the collision is given by its mass and velocity:

p_i = m * v_i = 1.2 kg * 15 m/s = 18 kg m/s

The hammer's final velocity after the collision can be found using the law of conservation of momentum, which states that the total momentum of an isolated system remains constant. We can write this as:

p_f = m * v_f = m * (-v_i * 0.6) = m * (-15 m/s * 0.6) = 9 kg m/s

The force experienced by the nail during the collision can be calculated as:

F = ma = (m * (v_f - v_i)) / t = (m * (9 kg m/s - 18 kg m/s)) / t

Since we know the force experienced by the nail is 9 000 N, we can use this to solve for t:

9 000 N = (1.2 kg * (9 kg m/s - 18 kg m/s)) / t

t = (1.2 kg * (9 kg m/s - 18 kg m/s)) / 9000 N

t = 0.00133 seconds

So the hammer is in contact with the nail for approximately 0.00133 seconds.

variable:

m: mass of the hammer, 1.2 kg

v_i: initial velocity of the hammer before the collision, 15 m/s

v_f: final velocity of the hammer after the collision, -9 m/s (negative sign indicates the direction of motion is opposite to the initial velocity)

t: duration of the hammer's collision with the nail, approximately 0

If the mass of an object is tripled while the force acting upon it is kept constant, the acceleration of the object will be reduced to one-third of its original value.

This can be explained using Newton's second law of motion, which states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.

In this scenario, the force is held constant, but the mass is increased by a factor of three. As a result, the acceleration will decrease by a factor of three, since the same force is now acting on a much heavier object. Therefore, the object will experience a lower acceleration than before, making it harder to move or change its speed or direction.

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The expressions which represent the electric potential difference between the two points due to the charge on the sphere  qQ/4πε0  (1/rb- 1/ra). (Option C)

The electric eventuality, also known as implicit drop or the electrostatic eventuality refers to the quantum of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field. The electric implicit generated from a point charge, Q, at a distance, r, from the position of Q is given by

V = 1/ 4πε0 Q/ r

When the electric eventuality is told by two point charge, Q and q, the formula is

V = 1/ 4πε0 qQ/ r

Electric implicit difference refers to the external work needed to bring a charge from one position to another position in an electric field. It's the change of implicit energy endured by a test charge that has a value of 1. The electric implicit difference is given as ΔV = Vb- Va

Hence, the expressions which represent the electric implicit difference between the two points due to the charge on the sphere qQ/ 4πε0( 1/ rb- 1/ ra).

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Complete question:

a particle of charge q is at point a , a distance ra from the center of a sphere of charge q . the particle is moved to point b , a distance rb from the center of the sphere. which of the following expressions represents the electric potential difference between the two points due to the charge on the sphere?

A) Q/4πε0  (1/rb- 1/ra) B) 1/4πε0   Q/rb C) qQ/4πε0  (1/rb- 1/ra) D) 1/4πε0   qQ/rb

Force is a physical quantity that describes the interaction between two objects, which can cause a change in the motion of an object. When a force is applied to an object, it can either cause the object to start moving, speed up, slow down, or change direction.

Force is typically measured in units of Newtons (N) and is represented by a vector, which has both magnitude (strength) and direction.

For example, pushing a book across a table requires a force that is applied in the direction of the push. If the force is strong enough to overcome the book's friction with the table, the book will begin to move in the direction of the force.

The amount of force required to produce a given effect on an object depends on several factors, including the mass of the object, the nature of the force, and the length of time the force is applied. In general, the greater the force applied to an object, the greater the acceleration (or deceleration) of the object.

Assuming that the force applied to an object is directly proportional to the acceleration it experiences, if the force were doubled, the acceleration would also double. This would result in a steeper slope on the acceleration vs. time graph.

As velocity is the integral of acceleration over time, if the acceleration were doubled, the velocity would increase at a faster rate than before. This would result in a steeper slope on the velocity vs. time graph.

Lastly, if the force applied to an object were doubled, the object would reach a higher velocity than before in the same amount of time. This would result in a higher maximum velocity and a longer time to come to a stop (assuming a constant force is applied). The velocity vs. time graph would shift upward and to the right, indicating a higher maximum velocity and a longer time to reach that maximum velocity.

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Answer:

C. The production of an electric current by a moving magnet

B. The production of a magnetic field by an electric current

What is electromagnetism?

The " real definition " of electromagnetism is the following:

Electromagnetism is the physical interaction among electric charges, magnetic moments, and the electromagnetic field.

There are different " types " of electromagnetic fields

The last thing that YOU should know is that electromagnetic waves are generally known as light and obey the laws of optics. Which means in similar terms they just obey the laws of optics.

Thus, the answers to your question is, C & B

Answer:

A

Explanation:

It is demonstrated that for each k, there exists a set of k positive integers whose difference has an even number of prime components, counted with multiplicity.

Let's construct the set of positive integers using the following algorithm:

Start with the first k prime numbers: 2, 3, 5, 7, 11, ..., p_k.

Define the i-th integer in the set as the product of the first i prime numbers: a_i = 235*...*p_i.

Claim: For any two integers in the set, their difference has an even number of prime factors, counted with multiplicity.

Proof:

Let a_i and a_j be two integers in the set such that i < j. We want to show that the difference a_j - a_i has an even number of prime factors, counted with multiplicity.

Notice that a_j - a_i can be written as:

a_j - a_i = 235*...p_i(235*...*p_j/2 - 1)

The first term on the right-hand side has i prime factors, and the second term has an odd number of prime factors. To see why the second term has an odd number of prime factors, notice that all the prime factors of 235*...p_j are also prime factors of 235...*p_i, so they cancel out in the difference.

a_j - a_i has i prime factors plus an odd number of prime factors, which is an even number of prime factors. This completes the proof.

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The exact order of steps used in every experiment of the scientific method.

The scientific method is defined as the process of making facts through testing and experimentation. The basic process includes making an observation, forming a hypothesis, making a prediction, carrying out an experiment, and then analyzing the results.

The six steps of the scientific method include asking a question about something doing background research about the topic, constructing a hypothesis, doing experiments to test the hypothesis, analyzing the data from the experiment, and making conclusions.

So we can conclude that option A is the correct answer.

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The muzzle velocity (VM) of a ball can be found by using a ballistic pendulum.

The basic principle of a ballistic pendulum is that the momentum of the ball before it hits the pendulum equals the momentum of the pendulum and the ball immediately after the collision.

The equation for this is

[tex]m_1v_1 = (m_1 + m_2) v_2[/tex]

, where m₁ is the mass of the ball, v₁ is the initial velocity of the ball, m₂ is the mass of the pendulum, and v₂ is the velocity of the pendulum and the ball immediately after the collision.

Solving for v₁, we get

[tex]VM = v_1 = (m_1 + m_2) \dfrac{v_2}{m_1}[/tex]

By measuring the height to which the pendulum rises and the mass of the pendulum, we can determine the velocity of the ball.

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The energy of each photon in electron volts is, 2.07.

Stopping potential is the minimum negative voltage applied to the anode to stop the photocurrent. The maximum kinetic energy of the electrons equal the stopping voltage, when measured in electron volt.

Stopping potential = Energy of light wave falling - energy of each photon

Energy of light wave falling = [tex]\dfrac{hc}{\lambda}[/tex]

Energy of light wave falling = [tex]\dfrac{hc}{\lambda}[/tex]

Energy in electron volts for a wave of wavelength 520 nm is, 2.37 eV.

Now,

Stopping potential = Energy of light wave falling - energy of each photon

0.3V = 2.37 - energy of each photon

Energy of each photon = 2.07

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The energy of the capacitor at this larger plate separation will be= D) U/4

The energy stored in a parallel-plate capacitor with plate area A, plate separation d, and charge Q is given by the formula:

U = (1/2) * (Q^2 / (ε_0 * A * d))

where ε_0 is the permittivity of free space.

If the separation between the plates is increased from d to 2d without changing the charge on the plates, the capacitance of the capacitor will be reduced by a factor of 2. This is because the capacitance of a parallel-plate capacitor is given by the formula:

C = ε_0 * A / d

So, when the separation is doubled, the capacitance is halved.

Since the charge on the plates remains constant, the energy stored in the capacitor is proportional to the square of the charge and inversely proportional to the capacitance. Thus, the new energy of the capacitor when the plates are separated by 2d is given by:

U' = (1/2) * (Q^2 / (ε_0 * A * (2d))) * (1/2)

where the factor of 1/2 is included because the capacitance is halved.

Simplifying this expression, we get:

U' = U / 4

Therefore, the energy of the capacitor at the larger plate separation is (d) U/4.

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The structure of the given paragraph about Ernest Cline is sequence writing.

The correct option is B.

Writing that organizes information or events in a certain order is known as sequence writing. In order for the reader to understand and follow the flow of events, sequence writing aims to convey information or events in a straightforward and logical manner.

For instance, the phases in a procedure are described sequentially in instructional writing to aid the reader in comprehending how to carry out a task. Events in narratives are presented chronologically to make it easier for the reader to follow the plot.

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The initial upward acceleration of the rocket is 15.75 m/s. The result is obtained using Newton's second law.

A rocket with a mass of 1.80 × 10⁴ kg is moving upward. The initial upward force produced by its engine (the thrust) is 4.60 × 10 N.

Find the initial upward acceleration without neglecting the gravitational force on the rocket!

We have

When the rocket moves upward, the acceleration can be found by Newton's second law equation.

F = ma

Without neglecting the gravitational force in the opposite direction, it will be

F - W = ma

F - mg = ma

With g = 9.8 m/s², the initial upward acceleration is

ma = F - mg

1.80 × 10⁴a = 4.60 × 10⁵ - 1.80 × 10⁴ × 9.8

1.80 × 10⁴a = 4.60 × 10⁵ - 1.764 × 10⁵

1.80 × 10⁴a = 2.836 × 10⁵

a =  1.575 × 10¹

a = 15.75 m/s

Hence, the rocket's initial upward acceleration is 15.75 m/s.

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A charge will flow until the electric field at the surface of the sphere is equivalent to the electric field of the test charge, because then the net force on all charges on the surface of the sphere will be zero. Here option B is the correct answer.

When the positive test charge is brought near the conducting sphere, the excess negative charge from the ground flows onto the surface of the sphere until equilibrium is reached. At this point, the electric field at the surface of the sphere becomes equal and opposite to the electric field of the test charge, thus canceling out the electric field of the test charge within the sphere.

Since the electric field inside the conductor is zero, the excess charges on the surface of the conductor are uniformly distributed and the net force on them is zero. Therefore, option B is the correct answer. Option A is incorrect because the excess charge on the surface of the sphere will be opposite in sign and not equal in magnitude to the test charge.

Option C is incorrect because the potential at the surface of the sphere is not necessarily the same as that of the test charge. Option D is incorrect because the excess charge on the surface of the sphere will be opposite in sign and not equal in magnitude to the test charge. Option E is incorrect because the net force on charges on the surface of the sphere is zero when the electric field at the surface of the sphere is equivalent to the electric field of the test charge.

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Assuming that the arrow is launched vertically upward with an initial velocity v and air resistance is negligible, the time the arrow is in the air until it returns to launch height can be expressed as:

t = 2v/g

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All of the electrical energy held in the capacitor is released as heat when it is fully discharged through the resistor.

Two conductors that are separated from one another and positioned close to one another make up a capacitor, an electrical energy storage device.A straightforward illustration of one such storage device is a parallel-plate capacitor.

The following formula can be used to determine how much energy was lost inside the resistor:

= ½ × ×

A parallel-plate capacitor's capacitance is determined by:

= × 0 × /,

Since the capacitor is charged until the stored electric energy is , we can write:

½ × × =

Solving for gives:

= 2 × /

Substituting this expression for into the formula for, we get:

½ × × ² × ( − 1)

(B) The potential difference across the capacitor will rise as long as the charging battery is still attached and the dielectric is inserted because of the higher capacitance. The following formula can be used to compute the new potential difference:

The capacitor's newly accumulated electrical energy is:

½ × × × ²

= ½ × × ² × ( − 1)

= ½ × × ² × ( − 1)

= ½ × × (² − ²)

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Question:

A parallel-plate vacuum capacitor is connected to a battery and charged until the stored electric energy is . The battery is removed, and then a dielectric material with dielectric constant is inserted into the capacitor, filling the space between the plates. Finally, the capacitor is fully discharged through a resistor (a resistor is connected across the capacitor terminals).

A) Find , the energy dissipated in the resistor.

Express your answer in terms of and other given quantities.

B)Consider the same situation as in the previous part, except that the charging battery remains connected while the dielectric is inserted. (Part B figure) The battery is then disconnected and the capacitor discharged. For this situation, what is , the energy dissipated in the resistor?

Express your answer in terms of and other given quantities.

Adam lifts a book from the floor, carries it across the room, and places it on a high shelf, he does work only while he carries the book across the room, which is in option B, as work = force x distance.

According to the equation for work (W = FD), work is only done when a force is applied to an object and it moves some distance as a result of that force, when Adam lifts the book from the floor, he applies force to it, but the book does not move any distance, so no work is done when the object doesn't move, but when he moved the book, work was done.

Hence, he does work only while he carries the book across the room, which is in option B, as he lifts a book from the floor and carries it across the room.

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(a) The final speed of the cooler is 5.77 m/s.

(b) In the presence of friction, the final speed of the cooler is 3.43 m/s.

The final speed of the cooler is calculated by applying work energy theorem as shown below;

Change in kinetic energy of the cooler = work done on the cooler

¹/₂mv² = fd

v² = (2fd) / m

v = √(2fd) / m

where;

The final speed of the cooler is calculated as;

v = √(2 x 30 x 2) / 3.6

v = 5.77 m/s

At the given coefficient of friction, the final speed is calculated as;

v = √(2Ffd) / m

where;

Ff = μW

where;

v = √(2μWd) / m

v = √(2 x 0.3 x 3.6 x 9.8 x 2) / 3.6

v = 3.43 m/s

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(a) Circumference is, C = 7.4π. (b) Time interval is, [tex]A_t = 0.089 s[/tex]. (c) Current value is, [tex]I = -1.80 \times 10^{-18} A[/tex]

Part (a): The circumference of a circle with radius R is given by C = 2πR. Therefore, for a circle of radius 3.7 m, we have:

[tex]C = 2\pi(3.7) = 7.4\pi[/tex]

[tex]Expression: C = 7.4\pi[/tex]

Part (b): The time interval At for electron to finish one circle is given by the distance traveled divided by the speed. In this case, the distance traveled is equal to the circumference of the circle, so we have:

[tex]At = C/v[/tex]

[tex]At = 7.4\pi/83[/tex]

[tex]A_t = 0.089 s[/tex]

Part (c): The current on the circle can be found using the formula [tex]I = Q/t,[/tex]where Q is the charge and t is the time interval. Since the electron has a charge of -e,

[tex]I = (-e)/At[/tex]

Substituting the value of At from above,

[tex]I = (-1.602 * 10^-19 C)/0.089 s[/tex]

[tex]I = -1.80 * 10^{-18} A[/tex]

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Two parallel conducting plates are charged with equal and opposite charges. Then the correct statement about the magnitude of the electric potential is greater at point B.

Here electric field exists between the positive and negative plates. Its direction will be from the positive plate to the negative plate. The electrostatic potential is the work done in moving a unit charge in the electric field. The relationship between the electric field and electric potential is electric field is the negative gradient of electric potential.

E = -dV/dr

V = -∫E.dr

E.dr = E×dr×cos(theta)

Here on moving from the positive plate to the negative plate Electric field and distance are in the same direction.

Hence the value of the angle theta between them will be 0 degrees. Then we will potential as negative. That is on moving from the positive plate to the negative plate potential decreases. So, point B near the positive plate is having higher potential compared to others.

Point A is outside the plates where the electric field and hence potential is zero.

This question is accompanied by an image and Option B is the correct one.

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The picture that best represents the charge distribution on the inner and outer walls of the shell is picture 4

Charge distribution on a conducting shell can affect the electric field both inside and outside the shell. If the charge is distributed uniformly on the surface of the shell, the electric field inside the shell will be zero, while the electric field outside the shell will be the same as that of a point charge located at the center of the shell.

If the charge is distributed non-uniformly, then the electric field inside and outside the shell will be affected accordingly. In general, the charge distribution will determine the potential difference between the inside and outside of the shell, which can have important implications for the behavior of charged particles both inside and outside the shell.

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Answer:1.13m

Explanation:

Potential Energy= mgh

m= mass(kg)

g= gravitational field strength(9.81m/s^2)

h= height

PE=mgh

PE= 2J

therefore: 2J= 0.180kg x 9.81 m/s^2 x h

       h= 2/(1.764)

       h= 1.13m

Electric field change if a third object with a charge +q is placed at point P2 is the magnitude of the electric field will decrease by 25%.

Electric field is a vector quantity. It has a direction towards the negative charge and away from a positive charge.

Due to the 2 negatice charges, electric field E's verticle component will add up and horizontal component will cancel each other.

Electric field due to a charge particle = K q / r^2

K = constant

q = charge

r = distance of the point from the charge

Angle made by electric field = 45 degrees

Verticle component of the electric field due to two -q = E =2 *  K(-q) cos 45 / (V2 R)^2 \

= -V2 Kq/2R^2 = -0.71 Kq/R^2

New electric field after a charge +q is introduced = initial E + E due to +q

E due to +q = Kq / (2R)^2 = 0.25 Kq/R^2

Percentage Change in electric field = (Change in electric field / Initial electric field) * 100 = 0.25 *100 / -0.71 = -25%.

Therefore, the magnitude of the electric field will decrease by 25%.

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The frequency and wave speed after the water was high in Toledo and low in Buffalo is 2.3 * 10^-5 Hz and 18 m/s

Period = 12 hours

= 43,200 seconds.

The number of cycles or vibrations that a body in periodic motion experiences during one unit of time, as well as the number of waves that pass a fixed point in a unit of time. After moving through a series of situations or positions and then returning to its initial position, a body in periodic motion is said to have experienced one cycle or one vibration.

Frequency= 1/T

= 1/43200

= 2.3 * 10^-5 Hz

The amount of space a wave covers in a certain amount of time, such as the number of metres it covers in a second, is known as its wave speed. Speed = Wavelength x Frequency is an equation that describes how wave speed relates to wave wavelength and wave frequency. When the wavelength and frequency are known, this equation can be used to determine the wave speed.

Wave speed

= wavelength*(1/period)

= wavelength*frequency

= 800,000 m * 2.3 * 10^-5 Hz

= 18 m/s

Therefore, wave speed of the water be 18 m/s.

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The bolt's initial velocity, V, is zero when it is released from the container at a height of 94 meters.

A height of 0.26*94 = 24.4 m marks the final 26% of its descent.

By then, the bolt had dropped 94 - 24.4 = 69.56 m.

The last 26% of the bolt's fall takes 0.6122 seconds to complete.

(b) The bolt travels at a speed of 36.92 m/s for the final 26% of its descent (nearest hundredth).

(c) The bolt's speed is 42.94 m/s just before it touches the earth (nearest hundredth).

The change in displacement is measured in terms of velocity. The rate of velocity that changes is known termed accelerated. Due to the magnitude it contains, velocity is a vector quantity.

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What is the velocity resulting from gravity here on surface of a star with a mass and diameter that are three times those of the earth (assuming that the earth's surface gravity is 9.8 m/s-2)

What is the ultimate speed?

The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction once it's reached maximum acceleration. How is the final velocity determined? It is easy to determine the final velocity with a few computations and little conceptual understanding.

What makes speed and velocity different from one another?

Most people mix the terms velocity and velocity in regular speech. These are different concepts that don't share the same significance in physics. Speed has no direction, which is one critical difference. Speed is therefore a scalar.

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