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

Answer:

$v = \sqrt{2gy}$

Explanation:

Formula for Kinetic Energy $E_k = \frac{mv^2}{2}$

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

$E_k = E_p$

$\frac{mv^2}{2} = mgy$

$v^2 = 2gy$

$v = \sqrt{2gy}$