Physics impulse and momentum question

Question

A Figure skater of mass 70kg is gliding at a velocity of 3.5 m/s [E]. Their skating partner, of mass 45 kg, skates at a velocity of 4.2 m/s [N] when they jump into the first skater’s arms. Determine the new velocity vector of the combined skaters as they complete the trick.

Answer 1

This is a 2D completely inelastic collision: momenta before = momentum afterward The momenta must be added vectorially. In this case, they are at right angles, so Pythagorean theorem applies:

p²_skater + p²_partner = p²_together

sqrt((m_sv_s)²+(m_pv_p)²)/(m_s+m_p) = v_together (Plug in values)