Question

Two cars (a and b) of equal mass have an elastic collision. Prior to the collision, car a is moving at 20m/s in the x-direction, and car b is moving at 10m/s in the -x direction. What will be the velocities of car a and car b after the collision?

Answer 1

In an elastic collision between two cars of equal mass, the final velocities are determined using the conservation of momentum equation. The velocity of car A after the collision will be -5 m/s in the x-direction, and the velocity of car B after the collision will be 5 m/s in the -x-direction.

Step-by-step explanation:

In an elastic collision, the total momentum of the system is conserved. Given that the two cars have equal masses, the final velocities can be calculated using the conservation of momentum equation:

mvAi + mvBi= mvAf + mvBf

Substituting the given values, we have:

20m + (-10m) = mvAf + mvBf

Simplifying the equation further:

10m = mvAf + mvBf

Since both cars have equal masses, we can write:

10m = 2mv

Dividing both sides by 2m:

5 = vAf + vBf

So, the sum of their final velocities will be 5 m/s. However, since the cars have opposite initial velocities, their final velocities will also be opposite in direction. Therefore, the velocity of car A after the collision will be -5 m/s in the x-direction, and the velocity of car B after the collision will be 5 m/s in the -x-direction.