Question

A planet has radius 3/2 that of the earth and a density of 1/3 that of the earth. If a man jumps 1.5m on the earth, the approximate height he might jump on the planet is?

Answer 1

The acceleration due gravity

$$g=G\frac{M}{R^2}=\frac{4}{3}\pi G\rho R$$

$$g=\frac{4}{3}\pi G\left(1/3\rho_E\right) (3/2R_E)=1/2g_E$$

The height that a man might jump on the planet

$$h=\frac{v_0^2}{2g}=\frac{v_0^2}{2(1/2g_E)}=2h_E=2*1.5\:\rm m=3 \: m$$