The acceleration due to gravity on planet A is 9 times the acceleration due to gravity on planet B. A person can jump to a height of 2m on the surface of A. What is the height of a jump by the same person on planet B?

Given, acceleration due to gravity on plane A is 9 times 

acceleration due to gravity on planet B i.e., ${\mathrm{g}}_{\mathrm{A}}=9{ \mathrm{g}}_{\mathrm{B}} \dots \left(\mathrm{i}\right)$

From third equation of motion

${\mathrm{v}}^2=2\mathrm{gh}$

$\text{ At planet }\mathrm{A},{\mathrm{h}}_{\mathrm{A}}=\frac{{\mathrm{v}}_2}{2{ \mathrm{g}}_{\mathrm{A}}} \dots \text{..(ii) }$

$\text{ At planet B},{\mathrm{h}}_{\mathrm{B}}=\frac{{\mathrm{v}}_2}{2{ \mathrm{g}}_{\mathrm{B}}} \text{.......(iii)}$

$\text{ Dividing Eq. (ii) by Eq. (iii) we have }$

$\frac{{\mathrm{h}}_{\mathrm{A}}}{{\mathrm{h}}_{\mathrm{B}}}=\frac{9{ \mathrm{g}}_{\mathrm{B}}}{9{ \mathrm{g}}_{\mathrm{A}}}$

$\text{ From Eq. (i), }{\mathrm{g}}_{\mathrm{A}}=9{\mathrm{g}}_{\mathrm{B}}$

$\therefore \frac{{\mathrm{h}}_{\mathrm{A}}}{{\mathrm{h}}_{\mathrm{B}}}=\frac{9{ \mathrm{g}}_{\mathrm{B}}}{9{ \mathrm{g}}_{\mathrm{A}}}=\frac{1}{9}$

$\text{ or }{\mathrm{h}}_{\mathrm{B}}=9{ \mathrm{h}}_{\mathrm{A}}=9\times 2 \left(\therefore {\mathrm{h}}_{\mathrm{A}}=2 \mathrm{m}\right)$

$=18 \mathrm{m}$