A45.0 kg girl is standing on a 159 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 1.38 m/s relative to the plank.
(a) what is her velocity relative to the surface of ice?
1 m/s
(b) what is the velocity of the plank relative to the surface of ice?
2 m/s

(a)

(b)

Explanation:

According to the law of conservation of momentum:

Initially, the girl and the plank are at rest. So, relative to the ice, we have:

(a) The velocity of the girl relative to the ice is:

Here, is the velocity of the girl relative to the plank and is the velocity of the plank relative to the ice.

Replacing (1) in (2):

(b) According to (2), the velocity of the plank relative to the surface of ice is:

The negative sing indicates that the plank is moving to the left.

causes

fossil fuels burn

cities become more industrialized

human population grows worldwide