Finding how much energy is lost and gained in...?

Question

Car 1 and 2 both weigh 1000kg,
Car 1 starts at top of 25m hill,
Car 2 starts on flat road,
Car 1 drives at 20m/s,
Car 2 drives at 30m/s, then comes to a stop.
Car 1 drives directly into 2 and the two cars end up moving in the same direction at 10m/s.

How much energy did Car 1 LOSE in the collision?
How much energy did Car 2 GAIN in the collision?

Please explain or write out the problem. Thank you.

Answer 1

The key step in this problem is to figure out the information you don't need.

Car 2 drives at 30 m/s - and then comes to a stop. This means that at the point of collision, Car 2 has no kinetic energy. Ignore the 30 m/s.

Car 1 may start at the top of a hill, but the problem does not tell you that the collision occurs on the hill, so you must assume that it occurs on the flat road. This means there's no potential energy gain/loss.

Step 2: Using what we learned from Step 1, set up the kinetic energy equations for the start and end:
Starting kinetic energy:
Car 2 stopped, so KE = 0
Car 1: m = 1000 kg, v = 20 m/s, KE = .5mv^2 = 200,000 J

Ending kinetic energy:
Car 1: m = 1000 kg, v = 10 m/s, KE = .5mv^2 = 50,000 J
Car 2: m = 1000 kg, v = 10 m/s, KE = .5mv^2 = 50,000 J

Car 1's ΔKE = 200 kJ - 50 kJ = - 150 kJ
Car 2's ΔKE = 0 + 50 kJ = 50 kJ