Question 16
The weight of a person on a planet A is about half that on the earth. He can jump upto 0.4 m height on the surface of the earth. How high he can jump on the planet A?

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Solution

Since, the weight of the person on planet A is half that on the earth, the acceleration due to gravity there will be $\frac{1}{2}$ that on the earth. Hence he can jump double the height with the same muscular force.
Or
The potential energy of the person will remain the same on the earth and on planet A.
Thus, $m g_{1} h_{1} = m g_{2} h_{2}$
$g_{1} = a c c e l e r e a t i o n d u e t o g r a v i t y o n e a r t h = g$
$g_{2} = a c c e l e r e a t i o n d u e t o g r a v i t y o n p l a n e t A$
$h_{1} = h e i g h t o n t h e s u r f a c e o f t h e e a r t h$
$h_{2} = h e i g h t o n t h e s u r f a c e o f p l a n e t A$

If $g_{1} = g$
then $g_{2} = \frac{1}{2} g$
$h_{1} = 0.4 m$
Then $h_{2} = \frac{g_{1} h_{1}}{g_{2}} = \frac{g \times 0.4}{\frac{g}{2}}$
or $h_{2} = 0.4 \times 2 = 0.8 m$

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Question 16 The weight of a person on a planet A is about half that on the earth. He can jump upto 0.4 m height on the surface of the earth. How high he can jump on the planet A?

Question 16
The weight of a person on a planet A is about half that on the earth. He can jump upto 0.4 m height on the surface of the earth. How high he can jump on the planet A?