Question

Car A is traveling at 35.0 mph. Car B starts from rest, pulls out of a parking lot, speeds up, and while texting on the phone and not looking at the road, crashes into Car A. If this is an elastic collision and both cars have 500.0-kg bumpers, what are the final velocities of each car? Neglect the mass of the drivers.

Answer 1

To solve this problem, we must use the laws of physics and the formulas for elastic collision.

Let's start by stating what we're given:

1. Car A has an initial velocity (v1_initial) of 35.0 mph, and Car B starts from rest, making its initial velocity (v2_initial) as 0.
2. Both cars have the same mass (m1 = m2 = 500.0 kg).

To work with these values, we first need to convert the initial velocity of Car A into meters per second as this is the standard unit we use in physics for such calculations. 1 mph equals approximately 0.44704 m/s, so to get the speed in m/s, we multiply the speed in mph by 0.44704.

Now, we employ the formulas of elastic collisions:

For the final velocity of Car A (v1_final), we use the formula:
v1_final = ((m1 - m2) / (m1 + m2)) * v1_initial

For the final velocity of Car B (v2_final), we use the formula:
v2_final = ((2 * m1) / (m1 + m2)) * v1_initial

Using these formulas, we find the result of the final speeds of both cars in m/s.

Finally, we convert the results back to mph by multiplying the answer by 2.23694, as 1 m/s is approximately 2.23694 mph.

Hence, the final velocities of Car A and Car B are 0.0 mph and 35.0 mph respectively after the collision, neglecting any minor rounding errors in calculations.

The outcome is unexpected but scientifically accurate: After the collision, Car A comes to a stop while Car B, which was initially at rest, now has the speed Car A had before the collision. This scenario will be true for any elastic collision where two objects of equal mass collide and one of them is initially at rest.