Question

A 45.0-kg girl is standing on a 166-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 1.48 m/s to the right relative to the plank. (Let the direction the girl is moving in be positive. Indicate the direction with the sign of your answer.)
1. What is her velocity relative to the surface of the ice?
2. What is the velocity of the plank relative to the surface of ice?

Answer 1

Answer:

-0.31563 m/s

1.16437 m/s

Explanation:

$m_1$ = Mass of girl = 45 kg

$m_2$ = Mass of plank = 166 kg

$v_1$ = Velocity of girl relative to plank = 1.48 m/s

$v_2$ = Velocity of the plank relative to ice surface

In this system the linear momentum is conserved

$(m_1+m_2)v_2+m_1v_1=0\\\Rightarrow v_2=-\frac{m_1v_1}{m_1+m_2}\\\Rightarrow v_2=-\frac{45\times 1.48}{45+166}\\\Rightarrow v_2=-0.31563\ m/s$

Velocity of the plank relative to ice surface is -0.31563 m/s

Velocity of the girl relative to the ice surface is

$v_1+v_2=1.48-0.31563=1.16437\ m/s$