1.A 2 kg rock is released from rest at a height of 29 m.Ignore air resistance and determine the kinetic energy,gravitational potential energy,and total mechanical energy at each of the following heights:20m; 15m; 5m; 9m.2.A man runs with a speed of 6

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1.A2kgrockisreleasedfromrestataheightof29m.Ignoreairresistanceanddeterminethekineticenergy,gravitati

1.A 2 kg rock is released from rest at a height of 29 m.Ignore air resistance and determine the kinetic energy,gravitational potential energy,and total mechanical energy at each of the following heights:20m; 15m; 5m; 9m.2.A man runs with a speed of 6
1.A 2 kg rock is released from rest at a height of 29 m.Ignore air resistance and determine the kinetic energy,gravitational potential energy,and total mechanical energy at each of the following heights:20m; 15m; 5m; 9m.
2.A man runs with a speed of 6 m/s off a platform that is 10 m above the water.How fast if he moving when he hits the water?Ignore air resistance.

1.A 2 kg rock is released from rest at a height of 29 m.Ignore air resistance and determine the kinetic energy,gravitational potential energy,and total mechanical energy at each of the following heights:20m; 15m; 5m; 9m.2.A man runs with a speed of 6
在29米处刚释放时候的总机械能：
E = mgH = 2kg * 10 m/s^2 * 29 m = 580 焦耳
石头在下落过程中,机械能守恒.因此不论在什么高度 总机械能（total mechanical energy） 都是 580 焦耳.取重力加速度约等于 10 m/s^2.
在 20 m高度处
重力势能gravitational potential energy
Ep = mgh = 2kg * 10m/s^2 * 20m = 400 焦耳
动能 kinetic energy
Ek = E - Ep = 580 - 400 = 180 焦耳
15 m高度处
Ep = 2 * 10 * 15 = 300 J
Ek = E - Ep = 580 - 300 = 280 J
9 m 高度处
Ep = 2 * 10 * 9 = 180 J
Ek = E - Ep = 580 - 180 = 400 J
5 m 高度处
Ep = 2 * 10 * 5 = 100 J
Ek = E - Ep = 580 - 100 = 480 J

人的水平速度保持不变,垂直方向上的速度 设为 V⊥.根据机械能守恒.
(1/2)*m* V⊥^2 = mgH
取重力加速度 g = 9.8 m/s^2
V⊥ = √(2gH) = (2*9.8*10)^(1/2) = 196^(1/2) = 14 m/s
因此落在水面时 的总速度大小为
V = (V⊥^2 + V‖)^(1/2) = (14^2 + 6^2)^(1/2)
= 232^(1/2)
= 15.2 m/s

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