To calculate the kinetic energy of the ball when it hits the ground, we need to use the formula:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Given:
Mass of the ball (m) = 5 kg
Height of the tower (h) = 12 m
First, let's calculate the velocity of the ball when it hits the ground using the concept of gravitational potential energy:
Gravitational Potential Energy (PE) = mass * gravity * height
PE = m * g * h
Where gravity (g) is approximately 9.8 m/s^2.
PE = 5 kg * 9.8 m/s^2 * 12 m
PE = 588 J
The gravitational potential energy is converted into kinetic energy when the ball falls, so:
KE = PE = 588 J
Now we can rearrange the formula to solve for the velocity:
KE = 1/2 * m * v^2
588 J = 1/2 * 5 kg * v^2
v^2 = (588 J * 2) / 5 kg
v^2 = 2352 J / 5 kg
v^2 = 470.4 J/kg
v ≈ √470.4 J/kg
v ≈ 21.7 m/s
Therefore, the kinetic energy of the ball on hitting the ground is 588 J, and the velocity of the ball when it hits the ground is approximately 21.7 m/s.