Question

Let m represent the ball’s mass, y represent the distance the ball falls, and v represent the ball’s final speed. Define the system to only include the ball and use the Work-Energy Theorem to find an expression for v in terms of the other variables given and any constants that are necessary

Answer 1

`v = √(2gy)`

Step-by-step explanation:

Formula for Kinetic Energy
`E_k = (mv^2)/(2)`

Formula for Potential Energy
`E_p = mgy` where g = 9.81 m/s

When the ball travels a distance y downward, its potential energy would be converted to kinetic energy. Hence, the ball loses altitude and gains speed

By law of total energy conservation

`E_k = E_p`

`(mv^2)/(2) = mgy`

`v^2 = 2gy`

`v = √(2gy)`