A 50 kg skater standing at rest on frictionless ice pushes their 2.5 kg skateboard away at 8.0 m/s. Calculate the skater's recoil speed.

Dynamics Challenge #8 — Conservation of Momentum

Momentum of a
skateboard push.

Dynamics Medium

Problem

A 50 kg skater stands at rest on frictionless ice and pushes their 2.5 kg skateboard away at 8.0 m/s. Calculate the skater’s recoil speed.

Skater mass\( 50\ \mathrm{kg} \)
Board mass\( 2.5\ \mathrm{kg} \)
Board speed\( 8.0\ \mathrm{m/s} \)
Initial stateboth at rest

Frictionless ice — nothing external touches the momentum.

Hint: the total momentum starts at zero and must stay there — whatever the board carries forward, the skater must carry backward: \( m_1 v_1 = m_2 v_2 \).

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Momentum of askateboard push.

Problem

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Momentum of a
skateboard push.