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## Relative velocity in free fall

If a person jumps out of a plane, and a few seconds later, another person jumps, why is it that the difference in their velocities stays the same? Shouldn’t it decrease because eventually, the first diver will reach maximum velocity, but the other diver will be slower at first, but then he reaches max. velocity as well…I’m not wording it the best way, but any help would be greatly appreciated :]

[Posted by Iris]

Both are examples for free fall. The velocity at any instant is given by v = gt

If for the first one, time = t and for the second who jumps after n seconds, time=t-n

Therefore, velocity of the first one at any instant, v1=gt

for second one, v2=g(t-n)

The difference in velocities,

v1-v2 = gn, which shows that the difference in velocity remains constant.

This is because, both are moving with the same acceleration and their velocities are increasing at the same rate

## Ball falls to earth, and earth moves to ball?!!

Sandeepan Dhar Choudhary asked:

“When the ball falls on the earth, the earth also moves up to meet it. But the motion of the earth is not noticeable. Explain why?”

Answer:

The force exerted by the ball on earth is same as the force exerted by the earth on the ball. The acceleration of the ball towards earth is approximately 10 m/s2.

The acceleration of earth towards the ball = force/mass of earth ≈ 10-23 m/s2

When the earth moves towards the ball with this acceleration, the time required to travel the distance will be very large. If we assume a distance of 1m, and from the equation

$S=ut+\frac{1}{2}at^{2}$

we get t ≈ 1012 seconds whereas the ball reaches the earth in 0.4 seconds

[warning]In a nut shell, we can say that we cannot notice the motion of earth towards the ball due to the extremely low value of acceleration of earth towards the ball.[/warning]

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