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

Question

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

TestHub · Accepted Answer

It is given that, acceleration due to gravity on plane $A$ is $9$ times the acceleration due to gravity on the planet $B$ , i.e.,

$g_{A} = 9 g_{B}$ .... (i)

From the 3rd equation of motion, we have

$v^{2} = 2 g h$

At planet $A$ ,

$h_{A} = \frac{v^{2}}{2 g_{A}}$ .... (ii)

At planet $B$ ,

$h_{B} = \frac{v^{2}}{2 g_{B}}$ .... (iii)

Dividing equation (ii) by equation (iii), we get

$\frac{h_{A}}{h_{B}} = \frac{g_{B}}{g_{A}}$

From equation (i), $g_{A} = 9 g_{B}$

$\frac{h_{A}}{h_{B}} = \frac{g_{B}}{9 g_{A}} = \frac{1}{9} \Rightarrow h_{B} = 9 h_{A} = 9 \times 2 = 18 m$

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