CHEGG 1. Phobos, a moon of Mars, is one of the fastest moving and closest moons relative to its parent planet. Phobos is moving closer to Mars every year and scientists believe that, eventually, Phobos will collide with Mars. Let's analyze the inevitable collision, given that the mass of Mars is 6.39 x 1023 kg, the mass of Phobos is 1.066z 1016 kg and all of the mass from Phobos stays attached to the surface of Mars after the collision. We will approximate the collision to be one dimensional, knowing that Mars is moving 24. 131 toward Phobos and Phobos is moving 19, 222 toward Mars (the opposite direction to the velocity of Mars). (a) (10 points) Determine the change in velocity of Mars, during the collision.

We can solve this exercise using the conservation of the moment. The system is formed by the satellite and the planet, so the forces in the collision are internal and the moment is preserved.

The data they give are the mass (m) and velocity (v₁) of Phobos and the mass (M) and velocity (v₂) of the planet

Initial moment before the collision, let's take as positive the direction in which the planet moves (Mars)

p₀ = m (-v₁) + M v₂

Final moment after the collision

[tex]p_{f}[/tex] = (m + M) v

p₀ = [tex]p_{f}[/tex]

m (-v1) + M v2 = (m + M) v

v = (-m v1 + M v2) / (m + M)

calculate

v = (-1.066 10 16 19222 + 6.39 10 23 24131) / (1.066 1016 + 6.39 1023)

v = (-2.049 10 20 + 15.4197 10 27) /6.39 1023)

v = 1.5419 1028 / 6.39 1023

v = 2,413 104 m / s

We see that the change in speed is imperceptible