Answer to Question #96852 in Classical Mechanics for Jake

Question

Ted and his iceboat (combined mass = 240 kg) rest on the frictionless surface of a frozen lake. A heavy rope (mass of 80 kg and length of 100 m) is laid out in a line along the top of the lake. Initially, Ted and the rope are at rest. At time t= 0, Ted turns on a wench which winds 0.5 m of rope onto the boat every second. a) What is Ted’s velocity just after the wench turns on?

Answer 1

a) From the conservation of momentum:

$$MV=mv$$

$$V=\frac{m}{M}v$$

$$V=\frac{80}{240}0.5=0.167\frac{m}{s}$$