Question

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

• A. $\frac{2}{3}m$
• B. $\frac{2}{9}m$
• C. $18m$
• D. $6m$

Answer 1

The correct option is C $18m$

here we use the equation, $v^2=u^2-2gh$, where$,v=$ the final velocity
$u=$initial velocity$,h=$height
$g=$acceleration due to gravity
Since the final velocity $v=0$, and initial velocity of jump is same on both planets,

$0=u^2-2g_A{h}_A\Rightarrow u^2=2g_A{h}_A.....\left(1\right)$
$0=u^2-2g_B{h}_B\Rightarrow u^2=2g_B{h}_B.....\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$
$h_B=\frac{g_A\times h_A}{g_B}\Rightarrow h_B=\frac{9}{1}\times 2=18m$