What is the Height at Which a Falling Ball Reaches a Velocity of 5.2 m/s?

In summary, the conversation discusses how to find the height above ground level at which a ball will be moving at 5.2 m/s after falling from rest at an initial height of 5m. The solution involves using the conservation of energy theorem and solving for the final height using algebra.
  • #1
maddief
3
0

Homework Statement


A ball falls from rest from an initial height of 5m above the ground. At what height above ground level will the ball be moving at 5.2 m/s?

Homework Equations


gravitational energy = mgh
kenetic energy=(1/2)mv^2

The Attempt at a Solution


I tried solving for both types of energy but I do not have mass so I am not sure how to solve. Please help!
 
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  • #2
What you want to do is try using the conservation of energy theorem:
Ki + Pi = Kf + Pf
It starts from rest so Ki = 0, we want to find hf, which is in Pf, so solve for that

In the end your equations should work out to be
m*g*hi - (1/2) * m *vf2 = mghf
Use algebra to solve for hf. You can see that all the masses cancel, so you don't need them, and the velocity you have is vf! Let me know if it works.
 
  • #3
Thank you! It worked!
 

Related to What is the Height at Which a Falling Ball Reaches a Velocity of 5.2 m/s?

1. What is momentum and how is it calculated?

Momentum is a measure of an object's motion. It is calculated by multiplying an object's mass by its velocity. The formula for momentum is: p = mv, where p is momentum, m is mass, and v is velocity.

2. What is work and how is it related to energy?

Work is the transfer of energy from one object to another. It is calculated by multiplying the force applied to an object by the distance the object moves in the direction of the force. Work and energy are closely related, as work is a way of transferring energy between objects. The unit for both work and energy is the joule (J).

3. How does kinetic energy differ from potential energy?

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or state. Kinetic energy is dependent on an object's mass and velocity, while potential energy is dependent on an object's position and the forces acting on it. Both types of energy are forms of mechanical energy.

4. Can energy be created or destroyed?

According to the law of conservation of energy, energy cannot be created or destroyed. It can only be transferred from one form to another. This means that the total energy in a closed system remains constant.

5. How is the principle of conservation of momentum applied in real-life situations?

The principle of conservation of momentum is applied in many real-life situations, such as collisions between objects. In a collision, the total momentum of the objects involved before the collision is equal to the total momentum after the collision, as long as there are no external forces acting on the system. This principle is also applied in rocket propulsion, where the momentum of the expelled gas propels the rocket forward.

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