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

Step-by-step 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=-(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`