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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

A Question From Relativity

Sreeram Asks:

“my question is on relativity.Let us say two persons,one is standing still and other is moving with uniform velocity in a straight line(in +ve x direction),both are carrying  a clock synchronized previously.For the moving person he is at rest and the other guy is moving away from him in the opposite direction(negative x direction).Both of them feel that clock of the other guy is moving slowly.let us say the moving guy never stops and he calls the other in telephone at some point of time and asks the
time in his clock.But he will find that clock with him,is actually faster.how can that happen?”

Answer:

Please note that the theory of relativity can  be applied only for velocities compared to that of light in vacuum (3 lakh km/s). The situation will be very much different when we travel at such velocities. So far we are able to accelerate only subatomic particles to this speeds (LHC).

 

 

A numerical from Centre of mass

Pearl asks:

Two objects, of mass 1 kg and 2 kg, are moving with velocities equal to +2 m/sec and -3 m/sec. The center of mass of the two objects is moving at velocity

Answer:

CodeCogsEqn

=(1×2+2x(-3)/(1+2)=(2-6)/3=-4/3=-1.33 m/s (-ve sign shows that the centre of mass will be moving in the direction of the second body)

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