Question

A 4723-kg asteroid orbits 4.1 × 108 m above the Earth. The asteroid runs into another stationary asteroid of equal mass and the two stick together. What is the resulting velocity?

Answer 1

To find the resulting velocity when the two asteroids stick together, we can use the principle of conservation of momentum.

The initial momentum of the first asteroid before the collision is given by the product of its mass (m1) and its velocity (v1):

Initial momentum of asteroid 1 = m1 * v1

Since the second asteroid is stationary, its initial momentum is zero.

After the collision, the two asteroids stick together and move with a common velocity (v2). The total mass of the system after the collision is the sum of the masses of the two asteroids (m1 + m2).

According to the conservation of momentum, the initial momentum of the system is equal to the final momentum of the system:

Initial momentum = Final momentum

m1 * v1 + 0 = (m1 + m2) * v2

Given:

m1 = m2 = 4723 kg

v1 = initial velocity of the first asteroid (unknown)

v2 = final velocity of the combined asteroids (unknown)

We can substitute these values into the equation and solve for v2:

4723 kg * v1 + 0 = (4723 kg + 4723 kg) * v2

4723 kg * v1 = 9446 kg * v2

Dividing both sides by 9446 kg:

v1 = 2 * v2

Therefore, the initial velocity of the first asteroid (v1) is twice the final velocity of the combined asteroids (v2).

Since the initial velocity of the first asteroid is not given, we cannot determine the resulting velocity (v2) without additional information.