Question

1. Two spaceships are travelling through space when one spaceship fires a missile at the other one at 0.821c.

a. What is the relative velocity of the two spaceships if the second spaceship observes the missile approaching at 0.943c?

b. Are the spaceships travelling toward each other or away from each other?

Answer 1

let v be the relative velocity of spaceships

then

v = v' - u / ( 1 - (v'u / c² ))

where u is the velocity at which missile was fired

so,

v = 0.943 c - 0.821 c / ( 1 - ( 0.943 * 0.821) )

v = 0.54 c

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As the velocity of missile as seen by second spacecraft is more than the velocity at which it was fired,

both the spaceships are approaching each other.