A man can jump to a height of 1.5 , m on a pl | vedclass

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(C) The height $H$ reached by a man jumping with initial velocity $u$ is given by $H = \frac{u^2}{2g}$.Since the initial velocity $u$ is constant,$H \

Vedclass · Accepted Answer

$18$

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(C) The height $H$ reached by a man jumping with initial velocity $u$ is given by $H = \frac{u^2}{2g}$.Since the initial velocity $u$ is constant,$H \propto \frac{1}{g}$,which implies $\frac{H_B}{H_A} = \frac{g_A}{g_B}$.The acceleration due to gravity is given by $g = \frac{4}{3} \pi G ho R$,so $g \propto ho R$.Given $ho_B = \frac{1}{4} ho_A$ and $R_B = \frac{1}{3} R_A$,we have $\frac{g_B}{g_A} = \frac{ho_B R_B}{ho_A R_A} = \left(\frac{1}{4}ight) 	imes \left(\frac{1}{3}ight) = \frac{1}{12}$.Therefore,$\frac{H_B}{H_A} = \frac{g_A}{g_B} = 12$.Thus,$H_B = 12 	imes H_A = 12 	imes 1.5 \, m = 18 \, m$.

$A$ man can jump to a height of $1.5 \, m$ on a planet $A$. What is the height he may be able to jump on another planet whose density and radius are,respectively,one-quarter and one-third that of planet $A$?

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