You throw a tennis ball (mass 0.0570 kg) vertically upward. it leaves your hand moving at 15.0 m/s. air resistance cannot be neglected, and the ball reaches a maximum height of 8.00 m. by how much does the total mechanical energy decrease from when the ball leaves your hand to when it reaches its maximum height?

It decreases 1.94 J.

Explanation:

At starting level, if we choose this height as our gravitational potential energy reference level, all the energy is kinetic:

E1 = K1 = 1/2 mv² = 1/2 . 0.057 Kg. 15² (m/s)² = 6.41 J

When it arrives to the maximum height (in this case, 8.0 m), all the energy has become gravitational potential energy, as the ball is at  rest just before starting to fall:

E2 = U2 = m.g.h = 0.057 kg. 9.8 m/s². 8.0 m = 4.47 J

The difference between these values is due to the effect of the air resistance, and can be expressed as follows:

ΔE = 6.41 J - 4.47 J = 1.94 J

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