Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / Section A / 2 / Solution

For equal mean mass densities, $M_a/M_E=(r/R_E{)}^3$. Thus the asteroid's surface gravitational acceleration is $g_a=g_{E}r/R_E$ and its escape speed isAn explicit estimate of jumping ability is an Earth jump height $H=0.50\mathrm{m}$, giving $v_J=\sqrt{2g_{E}H}\simeq 3.1\mathrm{m}{\mathrm{s}}^{-1}$. ConsequentlyThis is an order-of-magnitude estimate, scaling with assumed take-off speed; no unique human jump speed is supplied. A spherical nonrotating asteroid and negligible atmosphere are assumed.