Getting rear-ended

Ms. Chang is rear-ended at a stop light by Mr. Nelson, and sues to make him pay her medical bills. He testifies that he was only going 35 miles per hour when he hit Ms. Chang. She thinks he was going much faster than that. The cars skidded together after the impact, and measurements of the length of the skid marks and the coefficient of friction show that their joint velocity immediately after the impact was 19 miles per hour. Mr. Nelson's Nissan weighs 3100 pounds, and Ms. Chang 's Cadillac weighs 5200 pounds. Is Mr. Nelson telling the truth?

Since the cars skidded together, we can write down the equation for conservation of momentum using only two velocities, v for Mr. Nelson's velocity before the crash, and v0 for their joint velocity afterward:

Solving for the unknown, v, we find

Although we are given the weights in pounds, a unit of force, the ratio of the masses is the same as the ratio of the weights, and we find v = 51 miles per hour. He is lying.