Two manned satellites approach one another at a relative speed of 0.250 m/s, intending to dock. the first has a mass of 4.00×10^{3} kg, and the second a mass of 7.50×10^{3} kg. if the two satellites collide elastically rather than dock, what is their final relative velocity (in m/s)?

Explanation:

Let are initial speeds of satellite 1 and 2 and are final speeds of satellite 1 and 2 after collision respectively.

It is given that, the relative speed of two manned satellites is 0.25 m/s,

It is mentioned that thy collide elastically rather than dock, the momentum will remain conserved. So,

In elastic collision, the kinetic energy also remains conserved, so

For an elastic collision, the velocity of separation is equal to the velocity of approach such that, e = 1

(given )

So, their final relative velocity is 0.25 m/s. Hence, this is the required solution.

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