Question

Which of the following is a completely elastic collision?

A. a ball rebounds against a wall, reversing its direction, but at only half the speed.

B. Two balls collide, stick to each other, and move together after the collision.

C. Two balls collide and move at a right angle to each other after the collision at a reduced speed.

D. Two balls collide head on, each reversing its direction and traveling at half the speed.

E. A ball with velocity v collides with a ball at rest; after the collision the first ball is at rest and the second ball has velocity v.

I will mark brainliest

Answer 1

Hi there!

Answer E.

For a collision to be completely elastic, there must be NO LOSS in kinetic energy.

We can go through each answer choice:

A. Since the ball rebounds at half the initial speed, there is a loss in kinetic energy. This is NOT an elastic collision.

B. A collision involving sticking is an example of a perfectly INELASTIC collision. This is NOT an elastic collision.

C. A reduced speed indicates that there is a loss of kinetic energy. This is NOT elastic.

D. The balls traveling at half the speed after the collision indicates a loss of kinetic energy, making this collision NOT elastic.

E. This collision indicates an exchange of velocities, characteristic of an elastic collision. We can prove this:

Let:

m = mass of each ball

v = velocity

We have the initial kinetic energy as:

$KE = \frac{1}{2}mv^2 + 0 = \frac{1}{2}mv^2$

And the final as:

$KE = 0 + \frac{1}{2}mv^2 = \frac{1}{2}mv^2$

Thus, Kinetic energy is CONSERVED. This collision is ELASTIC.