All Problems

Laws of Conservation

Problem 1.156

Two men, each of mass mm, stand on the edge of a stationary buggy of mass MM. Assuming the friction to be negligible, find the velocity of the buggy after both men jump off with the same horizontal velocity u relative to the buggy (1) simultaneously; (2) one after the other. In what case will the velocity of the buggy be greater and how many times?

Reveal Answer
1.156. (1) v1=−2mM+2mu\mathbf{v}_{1}=-\frac{2 m}{M+2 m} \mathbf{u} (2) v2=−m(2M+3m)(M+m)(M+2m)u\mathbf{v}_{2}=-\frac{m(2 M+3 m)}{(M+m)(M+2 m)} \mathbf{u} v2/v1=1+m/2(M+m)>1v_{2} / v_{1}=1+m / 2(M+m)>1
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