A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space.The satellites collide and somehow manage to stick together.What is the speed of the combined object after the collision?
A)0.333c
B)0.374c
C)0.397c
D)0.418c
E)0.432c

Question

Quizplus · Accepted Answer

First, we need to find the total momentum of the system before the collision and after the collision. Since the satellites are traveling towards each other, the direction of the momentum is opposite for each satellite, meaning one is negative and one is positive. Using the formula for momentum, p=mvγ, we get:

p1 = -200 kg x 0.8c x 200 kg/sqrt(1-(0.8c)^2) = -64556.5 kg m/s

p2 = 100 kg x 0.6c x 200 kg/sqrt(1-(0.6c)^2) = 41515.2 kg m/s

Total momentum before collision: p1 + p2 = -23041.3 kg m/s

Since the satellites stick together, they become a single object with a mass of 300 kg (the sum of the original masses). To find the speed of the combined object after the collision, we can use the conservation of momentum equation: p = mvγ. Plugging in the values we know:

-23041.3 kg m/s = 300 kg x v x sqrt(1-v^2/c^2)

After solving for v, we get v = 0.418c.

Therefore, the answer is D.

A Satellite with a Rest Mass of 200 Kg and a Speed