In Fig.a man stands on a boat floating in still water. The mass of the man and the boat is 60 kg and 120 kg,respectively. a. If the man walks to the front of the boat and stops. what is the separation between the boat and the pier now? b. If the man moves at a constant speed of 3 m//s relative to the boat, what is the total kinetic energy of the system (boat + man)? Compare this energy with the kinetic energy of the system if the boat was tied to the pier.

In Fig.a man stands on a boat floating in still water. The mass of the

1.	In Fig.a man stands on a boat floating in still water. The mass of the man and the boat is 60 kg and 120 kg,respectively. a. If the man walks to the front of the boat and stops. what is the separation between the boat and the pier now? b. If the man moves at a constant speed of 3 m//s relative to the boat, what is the total kinetic energy of the system (boat + man)? Compare this energy with the kinetic energy of the system if the boat was tied to the pier.
Answer» Solution : a. DISPLACEMENT of MAN w.r.t boat `x_(m,b)=6m` `x_(b)=x_(m,b)(m_(1)/(m_(1)+m_(2)))=-6xx30/(60+20)=-2m` Therefore, boat displaces by `2 m` away from the PIER. `:.` Seperation `=2.5m` b. `vecv_(mb)=vecvm-vecvb` `m_(1)vecv_(m)+m_(2)vecv_(b)=0` `m_(1)(vecv_(mb)+vevcb)+m_(2)vecv_(b)=0` `m_(1)v_(mb)=(m_(1)+m_(2))v_(b)` `v_(b)=(m_(1)/(m_(1)+m_(2)))v_(mb)` `v_(b)=60/180xx3=1m//s` `KE` of the man `=1/2m_(m)v_(m)^(2)=1/2xx60xx(3-1)^(2)=120J` `KE` of the boat `=1/2xx120xx(1)^(2)=60J` TOTAL `KE` energy `=120+60=180J` `KE` of the sytem when the boat is tied `=1/2x60xx3^(2)=270J`