The moon's craters are remnants of meteorite collisions. suppose a fairly large asteroid that has a mass of 5.00×10^12 kg (about a kilometer across) strikes the moon at a speed of 15.0 km/s. at what speed does the moon recoil after the perfectly inelastic collision (the mass of the moon is 7.36×x10^22 kg)

Given:

Mass of asteroid, M1 = 5.00*10¹² kg

Velocity of asteroid V1 = 15.0 km/s

Mass of moon, M2 = 7.36*10²² kg

To determine:

The recoil velocity of moon, V2

Explanation:

Since the collision is perfectly inelastic, momentum is conserved. therefore,

M1 * V1 = M2* V2

V2 = M1*V1/M2 =  5.00*10¹² *15.0 /7.36*10²²  = 1.02*10⁻⁹ km/s

The moon will recoil at the speed of  1.02 x 10⁻⁹ km/s.

From the given question:

Therefore, we should determine V2

According to the question, supposing external forces acted on them (perfectly inelastic collision), then momentum is conserved. This also implies that their forces are equal and opposite in all instant.

Therefore, the law of conservation of momentum can express as:

M1 x V1 = M2 x V2

V2 = M1 x V1 / M2

If you substitute the value, then we have:

V2 = 5.00 x 10¹² kg x 15.0 / 7.36 x 10²² kg

V2 = 1.02 x 10⁻⁹ km/s.

Conservation of momentum basically describes Newton’s third of motion. It is commonly used to describe collision between two bodies. However, if two bodies collide with each other, the forces of these two bodies are the same and opposite at the same time.

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