The kids next door have asked you to help get their ball back, which accidentall

Question

The kids next door have asked you to help get their ball back, which accidentally landed on your roof. You help out and climb up to the roof to retrieve their ball. You throw the ball, which has a mass of 3.2 kg, off of the 5.6 m tall roof at a speed of 12 m/s.

What is the kinetic energy of the ball right after you throw it off of the roof? 230 J
What is the CHANGE IN gravitational potential energy of the "Ball and Earth" system from when the ball leaves your hand to just before it hits the ground? -176 J
What is the ball's speed right before it hits the ground? For now, ignore air resistance. 15.9 m/s
If friction is NOT negligible, and the ball lost 70 J to thermal energy as it fell to the ground, what is the ball's speed at the just before it hits the ground? 14 m/s

Explanation / Answer

KE = m v^2 /2 = 3.2 x 12^2 / 2 = 230.4 J

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PE = m g deta(h) = 3.2 x 9.81 x - 5.6

delta(PE) = -175.8 J

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Applying energy conservation,

PEi + KEf = PEf + KEf

175.8 + 230.4 = 0 + 3.2 v^2 /2

v = 15.9 m/s

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Energy lost = 70 J

KE = 175.8 +230.4 - 70

3.2 v^2 / 2 = 336.2

v = 14.5 m/s

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