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The acceleration due to gravity on 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 the jump by the same person on planet B?

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18 m

6 m

12 m

20 m

answer is A.

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Detailed Solution

The height of the jump by the same person on planet B will be

18 m .

It is given that acceleration due to gravity on planet A is 9 times the acceleration due to gravity on planet B.

g_{A} = 9 g_{B}

— (1)

g_{A}

= Gravity acceleration of planet A

g_{B}

= Gravity acceleration of planet B
From the third equation of motion

V^{2} = 2 gh

— (2)
At planet A,

h_{A} = \frac{V^{2}}{2 g_{A}}

— (3)
At planet B,

h_{B} = \frac{V^{2}}{2 g_{B}}

— (4)
Dividing equation (3) by (4) then we have,

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

\Rightarrow \frac{h_{A}}{h_{B}} = \frac{g_{b}}{9 g_{b}}

\Rightarrow \frac{h_{A}}{h_{B}} = \frac{1}{9}

\Rightarrow h_{B} = 9 h_{A}

\Rightarrow h_{B} = 9 \times 2

( since, hA = 2m)

\Rightarrow h_{B} = 18 m

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