Jon P. answered • 04/17/15

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Studied honors physics at Harvard, worked with many physics students

1. There are 2.2 kg in a pound at the surface of the earth, so his weight is 187 pounds.

2. Work is force times distance, if the force is constant. The force he exerts in climbing is mg, where m = 85 kg, and g = 9.8 kg-m/s

^{2}, so mg = 833 N. The distance he climbs is 15 m, so the amount of work he does is 833*15 = 12495 J.3. The potential energy from gravity at a height of h is mgh, where m is his mass and again h is 9.8 kg-m/s

^{2}. So in climbing to a height of 15 m, he has added 85 * 9.8 * 15 = 12495 J.4. Since he climbed in 22 seconds, his power was 12495 / 22 = 567.95 watts

5. The kinetic energy of his jump is 1/2 mv

^{2}= 1/2 * 85 * 6^{2}= 1530 J6. 1530 J of kinetic energy is completely converted to potential energy at the top of his jump. So 1530 = mgh = 85 * 9.8 * h = 833 h. So h = 1530 / 833 = 1.837 meters above the board.

7. Since the board is 15 m, his maximum height above the water is 16.837 m.

8. The total energy at the maximum height is the total potential energy added by the climb (12495 J) plus the potential energy added by his jump (1530 J). So the total potential energy at the maximum height is 14025.

9. The potential energy relative to the height of the water is all converted to kinetic energy when he splashes in. So 1/2 mv

^{2}= 14025. Solve this for v...1/2 mv

^{2}= 140251/2 * 85 v

^{2}= 14025v

^{2}=330v = 18.166 m/s