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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