# Conservation of momemntum and relative velocities

This is a problem about relative velocities and conservation of momemtum.

Here is how the problem goes:

A 39.7 kg girl is standing on a 101 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless supporting surface. The girl begins to walk along the plank at a constant speed of 1.58 m/s to
the right relative to the plank.

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

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

Working:

The way i'm thinking is that since the girl is moving to the right with a speed v=1.58 m/s then the plank moves (after being at rest) with the same speed v=1.58m/s but in the opposite direction (left) so its more like that the speed of the plank is -1.58 m/s.
Considering that, the ice surface is moving to the right with the same but opposite speed v, which is then 1.58 m/s.

Kinda sounds weird to me. I tried using conservation of momemntum also and said that:

(39.7)(1.58) + (101)(0) = 39.7(V) + (101)(-1.58)
then V is about 5.59 m/s

As for part B, i haven't been able to figure that one out. I dont know if conservation of momemtum should be used or some other method to solve it.

Help is greatly appreciated

Fangs

aww no replies yet

well i found something out but i'm not sure if i understood it correctly from my text book

the speed of the girl relative to the plank doesn't it mean:
Vg - Vp = 1.58

where Vg is the speed of girl and Vp is the speed of the plank

help is greatly appreciated

Doc Al
Mentor
the speed of the girl relative to the plank doesn't it mean:
Vg - Vp = 1.58

where Vg is the speed of girl and Vp is the speed of the plank
That's correct. Vg and Vp are the speeds of the girl and plank with respect to the ice. Now write the equation for conservation of momentum. You'll have two equations and two unknowns--solve!