Question

The moon's craters are remnants of meteorite collisions. Suppose a fairly large lasteroid that has a mass of 4.9x10¹²kg (such an asteroid is about a kilometer across) strikes the moon at a speed of 12.5km/s relative to the moon. At what speed, in meters per second, does the moon recoil after the perfectly inelastic collision? The mass of the moon is 7.36x10²².

Answer 1

To find the recoil speed of the moon after the collision, we can use the principle of conservation of momentum. We can plug the given values into the equation and solve for the recoil velocity. The recoil velocity of the moon after the perfectly inelastic collision is approximately 8.25 m/s.

Step-by-step explanation:

To find the speed at which the moon recoils after the perfectly inelastic collision, we can use the principle of conservation of momentum. Since the collision is perfectly inelastic, the asteroid and the moon will stick together after the impact. Therefore, the initial momentum of the system is given by the sum of the momentum of the asteroid and the moon, and the final momentum is given by the sum of their combined mass multiplied by the recoil velocity.

Mathematically, we can express this as:

(Mass of asteroid * Velocity of asteroid) + (Mass of moon * 0) = (Mass of asteroid + Mass of moon) * Recoil velocity of moon

Plugging in the values:

(4.9 x 10^12 kg * 12.5 km/s) + (7.36 x 10^22 kg * 0) = (4.9 x 10^12 kg + 7.36 x 10^22 kg) * Recoil velocity of moon

Simplifying the equation:

Recoil velocity of the moon ≈ 8.25 m/s