Question

Tom Sawyer runs 10 m/s down the dock and leaps on to his floating raft already moving 1.5 m/s away from shore. If Tom weighs 70 kg and the raft weighs 130 kg, what speed will they both be moving? A. 895 kg m/sB. 11.5 m/sC. 6.4 m/sD. 5.75 m/s

Answer 1

Not the right answer in the options, speed is 4.47 m/s, and the procedure is coherent with option A

Step-by-step explanation:

Answer A uses mass and velocity units, which are momentum units. By using the conservation of momentum:

.
`p_(initial) =p_(final) \\m_(Tom)*v_(Tom)+m_(raft)*v_(raft)=(m_(Tom)+m_(raft))*v_(both) \\70*10+130*1.5 kg*m/s=895kg*m/s\\v_(both)=(895 kg*m/s)/(200 kg) =4.47 m/s`

Since Tom stays in the raft, then both are moving with the same speed. From the options, the momentum is in agreement with option A, however, the question asks for speed.