Elastic and Inelastic Collisions?

Question

anthony and sara are participating in the "Roll-a-Roma" rollerskating dance championship. While 75 kg Anthony rollerskates backwards at 3 m/s, 60 kg Sara jumps into his arms with a velocity of 5 m/s in the same direction

a). how fast does the pair roll backwards together?

b). If Anthony is skating toward sara when she jumps, would their combined final velocity be larger or smaller than your answer to part A?

Answer 1

a)
m1v1+m2v2=(m1+m2)v
v=[m1v1+m2v2]/(m1+m2)

b)
m1v1-m2v2=(m1+m2)v
v=[m1v1-m2v2]/(m1+m2)
In this case velocity will be smaller since momentum is a vector and the Anthony's momentum is subtracted from Sara's.