While the ball is held 20 meters above the floor,
Potential energy = (mass) (gravity) x (height) =
(0.5 kg) x (9.8 m/s²) x (20 m) = 98 joules.
When it's dropped and reaches 1/2 of its initial height, it has half as much
potential energy. The rest has turned into kinetic energy = 49 joules.
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Kinetic energy = (1/2) x (mass) x (speed)²
49 joules = (1/2) x (0.5 kg) x (speed)²
Divide each side by (0.25 kg): 49 joules / 0.25 kg = speed²
Take the square root of each side: 7/0.5 = speed = 14 meters per second
That's the speed of the ball after falling 10 meters !
How cool is that !