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Classical Mechanics Level 2

When a $1$ kg mass is thrown down from the top of a building which is $20$ m high, it hits the Earth with a speed of $20$ m/s.

What would be the speed if this was carried on another planet where the acceleration due to gravity is $\dfrac{1}{4}$ of the Earth?

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1.25 5 2.5 7.5 10

1 solution

X X
Nov 4, 2018

Let the acceleration due to gravity on earth be $g$ .

If the time it falls on earth is $t_1$ , then the distance it falls is $0.5gt_1^2=20$ , the velocity when it hits the ground is $gt_1=20$ .

So $g=10,t_1=2$

If the time it falls on the other planet is $t_2$ , then the distance it falls is $0.5\times\frac g4\times t_2=20$ .

$t_2=4$ , the velocity when it hit the ground is $4\times2.5=10$