Question

The moon’s craters are remnants of meteorite collisions. suppose a fairly large asteroid that has a mass of 4.20×1012 kg (about a kilometer across) strikes the moon at a speed of 20.0 km/s. at what speed does the moon recoil after the perfectly inelastic collision (the mass of the moon is 7.36×1022 kg). how much kinetic energy is lost in the collision? a) 2.78 × 10^29 J

b) 3.15 × 10^29 J
c) 4.21 × 10^29 J
d) 5.93 × 10^29 J

Answer 1

The Moon recoils after the collision with a final speed of 2.79x10^-15 m/s. The collision causes a kinetic energy loss of 8.4x10^26 J.

Step-by-step explanation:

To find the speed of the Moon after the collision, we can use the principle of conservation of momentum. In a perfectly inelastic collision, the sum of the initial momenta is equal to the final momentum. Therefore, we can write:

(mass of asteroid x speed of asteroid) + (mass of Moon x 0) = (mass of asteroid + mass of Moon) x final speed

Plugging in the given values, we can solve for the final speed:

(4.20x10^12 kg x 20.0 km/s) + (7.36x10^22 kg x 0) = (4.20x10^12 kg + 7.36x10^22 kg) x final speed

Final speed = 2.79x10^-15 m/s

To find the kinetic energy lost in the collision, we can use the equation for kinetic energy:

Kinetic energy lost = initial kinetic energy - final kinetic energy

Using the given values, we can calculate the initial kinetic energy:

Initial kinetic energy = (0.5 x mass of asteroid x (speed of asteroid)^2)

Initial kinetic energy = 0.5 x 4.20x10^12 kg x (20.0 km/s)^2

Initial kinetic energy = 8.4x10^26 J

Since the final speed of the Moon is nearly zero, we can consider the final kinetic energy to be zero:

Final kinetic energy = 0 J

Therefore, the kinetic energy lost in the collision is:

Kinetic energy lost = 8.4x10^26 J - 0 J = 8.4x10^26 J