A spring launcher gives a 0.5 kg ball 25 J of kinetic energy, firing it straight up. Taking g = 9.8 m/s² and ignoring air resistance, calculate the maximum height the ball reaches.

Dynamics Challenge #6 — Energy Conservation

The 25-joule
launch.

Dynamics Hard

Problem

A spring launcher gives a 0.5 kg ball exactly 25 J of kinetic energy, firing it straight up. Calculate the maximum height the ball reaches.

Ball mass\( m = 0.5\ \mathrm{kg} \)
Kinetic energy\( E_k = 25\ \mathrm{J} \)
Gravity\( g = 9.8\ \mathrm{m/s^2} \)
Answer inmetres

Ignore air resistance — every joule of motion becomes a joule of height.

Hint: at the top, all 25 J have turned into gravitational potential energy: \( E_k = mgh \). You never need the launch speed — though it happens to be a clean number.

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The 25-joulelaunch.

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The 25-joule
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