Question

A 45.0 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

Answer 1

Answer:

Explanation:

Given

Mass of girl $m=45 kg$

Mass of Plank $M=159 kg$

let $v_p$ and $v_g$ be the velocity of Plank and girl w.r.t ice

therefore $v_{gp}=1.38 m/s$

Conserving Momentum

$(M+m)v_p+mv_{gp}=0$

$(45+159)v_p=-45\cdot v_{gp}$

$v_p=-\frac{45}{204}\cdot 1.38$

$v_p=-0.304 m/s$

$v_{gp}=v_g-v_p=1.38$

$v_g=-0.304+1.38=1.075 m/s$