Question

A heavy vehicle moving with velocity 15 m/s strikes an object of very small mass at rest head on elastically. Velocity of object after collision is

A. 15 m/s
B. 25 m/s
C. 20 m/s
D. 30 m/s

Answer 1

Correct option: A. 15 m/s

The velocity of the object after the collision is 15 m/s in the +x-direction, the same as the velocity of the heavy vehicle before the collision. This is because the collision is elastic and momentum is conserved.

Step-by-step explanation:

In an elastic collision, both momentum and kinetic energy are conserved.

Using the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

1. Let the mass of the heavy vehicle be M and the mass of the small object be m.
2. Since the heavy vehicle strikes the small object head-on, the initial velocity of the heavy vehicle is 15 m/s in the +x-direction, and the small object is at rest (0 m/s).
3. After the collision, let the velocity of the heavy vehicle be V and the velocity of the small object be v.
4. Applying the principle of conservation of momentum, we have: M * 15 m/s = M * V + m * v
5. Since the small object is initially at rest, its initial momentum is zero.
6. Therefore, the equation becomes: M * 15 m/s = M * V
7. Cancelling the mass, we have: 15 m/s = V

Therefore, the velocity of the small object after the collision is 15 m/s, which is the same as the velocity of the heavy vehicle before the collision.