Two manned satellites approach one another at a relative velocity of v = 0.150 m/s, intending to dock. the first has a mass of 4.00 * 103 kg, and the second a mass of 7.50 * 103 kg. if the two satellites collide elastically rather than dock, what is their final relative velocity?

Question

Physics

Bradshaw

2 July, 17:15

Two manned satellites approach one another at a relative velocity of v = 0.150 m/s, intending to dock. the first has a mass of 4.00 * 103 kg, and the second a mass of 7.50 * 103 kg. if the two satellites collide elastically rather than dock, what is their final relative velocity?

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Dillon Duran · Answer 1

Refer to the diagram shown below.

The relative velocity before the collision is 0.15 m/s. Therefore consider one satellite to be at rest and the other satellite to have a velocity of 0.15 m/s.

The total momentum before impact is

P₁ = (4000 kg) * (0.15 m/s) = 600 kg - (m/s)

After elastic impact, the rebound velocities are 0.15 m/s and u m/s.

The total momentum after impact is

P₂ = (4000 kg) * (-0.15 m/s) + (7500 kg) * (u m/s) = - 600 + 7500u kg - (m/s)

Because momentum is conserved, therefore

-600 + 7500u = 600

u = 1200*7500 = 0.16 m/s

The relative velocity after impact is

0.16 - (-0.15) = 0.31 m/s

Note: In elastic impact, there is no loss of kinetic energy.

Answer: 0.31 m/s