College

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 the ice?

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

Answer :

Answer:

Explanation:

Given

Mass of girl [tex]m=45 kg[/tex]

Mass of Plank [tex]M=159 kg[/tex]

let [tex]v_p[/tex] and [tex]v_g[/tex] be the velocity of Plank and girl w.r.t ice

therefore [tex]v_{gp}=1.38 m/s[/tex]

Conserving Momentum

[tex](M+m)v_p+mv_{gp}=0[/tex]

[tex](45+159)v_p=-45\cdot v_{gp}[/tex]

[tex]v_p=-\frac{45}{204}\cdot 1.38[/tex]

[tex]v_p=-0.304 m/s[/tex]

[tex]v_{gp}=v_g-v_p=1.38[/tex]

[tex]v_g=-0.304+1.38=1.075 m/s[/tex]

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