A ball of mass 20 g falls from a height of 45 m. It rebounds from the ground to a height of 40 m. Calculate :
the speed of the ball at which it hits the ground.
Topic: Conversion of potential energy to kinetic energy
Answer
Given: h = 45 m, g = 10 m s⁻²
As the ball falls, its potential energy becomes kinetic energy: ½ m v² = m g h
The mass cancels from both sides: ½ v² = g h v² = 2 g h = 2 × 10 × 45 = 900 v = √900 v = 30 m s⁻¹
Speed of the ball on hitting the ground = 30 m s⁻¹
The mass cancels, which is worth noticing: a heavy ball and a light one dropped from the same height hit the ground at the same speed, air resistance aside.
Take the square root at the end. Stopping at 900 gives v² rather than v, and 900 m s⁻¹ would be faster than sound — a size check that catches the error.
You could also check with the 9 J from part (a): ½ × 0.02 × 30² = 0.01 × 900 = 9 J ✓. All the potential energy has become kinetic energy.