Question

A 72-kg boy and a 48-kg girl, both wearing ice skates face each other at rest on a skating rink. The boy pushes the girl, sending her eastward with a speed of 6.8 m/s. What is the speed and direction of the boy?

Answer 1

Using conservation of momentum:

`\begin{gathered} P1=P2 \\ m1v1+m2v2=m1v1+m2v2 \\ where: \\ m1=72kg \\ m2=48kg \\ v2=+6.8m/s \end{gathered}`
`\begin{gathered} P1=P2 \\ m1u1+m2v1=m1u2+m2v2 \\ u1=0 \\ v1=0 \\ where: \\ m1=72kg \\ m2=48kg \\ v2=+6.8m/s \end{gathered}`

Solve for u2:

`\begin{gathered} 0=72u2+48(6.8) \\ 0=72u2+326.4 \\ u2=-(326.4)/(72) \\ u2=-4.5m/s \end{gathered}`

Answer:

4.5 m/s to the west