Question

Two asteroids in outer space collide, and stick together. The mass of each asteroid, and the velocity of each asteroid before the impact, are known. To find the momentum of the stuck-together asteroids after the impact, what approach would be useful?
(1) Use the Energy Principle.
(2) Use the Momentum Principle.
(3) It depends on whether or not the speed of the asteroids was near the speed of light.
(4) Use the relationship among velocity, displacement, and time.
(5) It depends on whether the collision was elastic or inelastic.

Answer 1

Answer: (2) Use the Momentum Principle.

Explanation:

In fact, it is called the Conservation of linear momentum principle, which establishes the initial momentum $p_{i}$ of the asteroids before the collision must be equal to the final momentum $p_{f}$ after the collision, no matter if the collision was elastic or inelastic (in which the kinetic energy is not conserved).

In this sense, the linear momentum $p$ of a body is defined as:

$p=mV$

Where $m$ is the mass and $V$ the velocity.

Therefore, the useful approach in this situation is option (2).