A 0.400-kg ice puck, moving east with a speed of 5.86 m/s , has a head-on collision with a 0.900-kg puck initially at rest. A. Assume that the collision is perfectly elastic, what will be the speed of the 0.300 kg object after the collision?
B. What will be the direction of the 0.300 kg object after the collision?
C. What will be the speed of the 0.900 kg object after the collision?

a) The final speed of the 0.400-kg puck after the collision is 2.254 meters per second, b) The negative sign of the solution found in part a) indicates that 0.400-kg puck is moving westwards, c) The speed of the 0.900-kg puck after the collision is 3.606 meters per second eastwards.

Explanation:

a) Since collision is perfectly elastic and there are no external forces exerted on pucks system, the phenomenon must be modelled after the Principles of Momentum and Energy Conservation. Changes in gravitational potential energy can be neglected. That is:

Momentum

Energy

Where:

, - Masses of the 0.400-kg and 0.900-kg pucks, measured in kilograms.

, - Initial speeds of the 0.400-kg and 0.900-kg pucks, measured in meters per second.

, - Final speeds of the 0.400-kg and 0.900-kg pucks, measured in meters per second.

If , , , , the system of equation is simplified as follows:

Let is clear in first equation:

Now, the same variable is substituted in second equation and resulting expression is simplified and solved afterwards:

There are two solutions:

or

The first root coincides with the conditions before collision and the second one represents a physically reasonable solution.

Now, the final speed of the 0.400-kg puck is: ()

The final speed of the 0.400-kg puck after the collision is 2.254 meters per second.

b) The negative sign of the solution found in part a) indicates that 0.400-kg puck is moving westwards.

c) The speed of the 0.900-kg puck after the collision is 3.606 meters per second eastwards.