A 50 kg person standing still in ice skates throws their 2.0 kg helmet to the right at 25 m/s while on a frictionless surface. What is the final speed ?

Answer 1

The initial total momentum of the player (mass is m_p= 50 kg) and helmet (mass is m_h is 2 kg) is

p_{total initial} = m_pv_{p iniitial} + m_hv_{h initial} where v_{p iniitial} and v_{h initial} are their initial velocities.

p_{total initial} = 0 because the player and helmet's velocities are zero, because they are both stationary.

Now the final total momentum is

p_{total final} = m_pv_{p final} + m_hv_{h final} where v_{p final} and v_{h final} are their final velocities.

v_{h final} = 25 m/s and using the masses

p_{total final} =(50 kg) v_{p final} + (2 kg) (25 m/s)=(50 kg) v_{p final} + 50 kgm/s

Now the net EXTERNAL force acting on the player and helmet is zero, so that means their total momentum will not change -> conservation of momentum.

so p_{total final} = p_{total final}

(50 kg) v_{p final} + 50 kgm/s = 0

Solving for v_{p final}

(50 kg) v_{p final} + 50 kgm/s = 0 => (50 kg) v_{p final} = -50 kgm/s

v_{p final} = (-50 kgm/s)/50kg = -1 m/s (the minus sign indicated the player is moving in the opposite direction relative to the helmet).