Question

A 45.0 kg girl is standing on a 163 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.45 m/s relative to the plank.

(a) What is her velocity relative to the surface of ice?

(b) What is the velocity of the plank relative to the surface of ice?

Answer 1

If the girl is walking at 1.45 m / s in the x direction relative to the plank and the plank is moving at velocity V in the x direction then her total velocity is 1.45 + V in the x direction. (note - V better come out negative, in the negative x direction in part b)

There are no external horizontal forces on this system.
Therefore there will be no change in the initial horizontal momentum, which is zero.
final momentum:
0 = 45 * (1.45+V) + 163 V
0 = 65.25 + 45 V + 163 V
208 V = - 65.25
V = -0.314 m/s

by the way that means the girl is going at 1.45 -.314 = 1.14 relative to the ice and as a check in the ice coordinate system
0 = -0.314 * 163 + 1.14 * 45 ???
= -51.2 + 51.3 close enough