Answer :
Final answer:
The velocity of the satellite after the collision is 5000 m/s.
Explanation:
The final velocity of the satellite after the collision can be calculated using the principle of conservation of momentum. Since the satellite and the space debris have the same mass and the space debris has a velocity of 3700 m/s after the collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the mass of the satellite and the space debris as m. The initial velocity of the satellite is 3700 m/s and the initial velocity of the space debris is 5000 m/s. After the collision, the velocity of the satellite is v and the velocity of the space debris is 3700 m/s.
Using the conservation of momentum, we can write:
(mass of satellite) x (initial velocity of satellite) + (mass of debris) x (initial velocity of debris) = (mass of satellite) x (final velocity of satellite) + (mass of debris) x (final velocity of debris)
Plugging in the given values:
(m) x (3700) + (m) x (5000) = (m) x (v) + (m) x (3700)
Simplifying the equation:
3700m + 5000m = vm + 3700m
8700m = vm + 3700m
8700m - 3700m = vm
5000m = vm
v = 5000 m/s
Therefore, the velocity of the satellite after the collision is 5000 m/s.
