An 800-kg car moving at 80 km/h collides head-on with a 1200-kg car moving at 40 km/h in the opposite direction. If they stick together, the wreckage now has an initial speed of

Question

Quizplus · Accepted Answer

The initial momentum of the system must equal the final momentum, since momentum is conserved. Convert speeds to m/s: 80 km/h = 22.22 m/s, 40 km/h = 11.11 m/s. Initial momentum = (800 kg * 22.22 m/s) + (1200 kg * -11.11 m/s) = 0. The final momentum = (800 kg + 1200 kg) * v. Since the initial momentum is 0, the final velocity v must also be 0, meaning the wreckage is stationary, which is not an option given. However, considering the direction and the relative speeds, the correct approach involves calculating the net momentum before the collision and setting it equal to the momentum of the combined mass after the collision, leading to a non-zero speed. Let's correct the calculation:Initial momentum = (800 kg * 22.22 m/s) - (1200 kg * 11.11 m/s) = 17776 - 13332 = 4444 kg*m/s. For the combined mass, 2000 kg * v = 4444 kg*m/s, solving for v gives v = 2.22 m/s, which is approximately 8 km/h when converted back to km/h. This indicates a mistake in my initial explanation regarding the system being stationary; the correct approach indeed shows that the system has a non-zero velocity post-collision, which corresponds to choice A when corrected for the proper calculation and understanding of momentum conservation.

An 800-Kg Car Moving at 80 Km/h Collides Head-On with a 1200-Kg