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Question

A man of mass M=50 kg is standing at one end of a boat of mass m=300 kg floating on still water. He walks towards the other end of the boat with a constant velocity (v=2 m/s) with respect to a stationary observer on land. Choose the correct options.


Correct Answer
A
Velocity of COM will be zero 
Your Answer
B
COM will move with constant velocity. 
Correct Answer
C
The magnitude of relative velocity of the boat with respect to the walking man is greater than the magnitude of the relative velocity of the boat w.r.t. the stationary observer. 
Your Answer
D
The magnitude of relative velocity of the boat with respect to the walking man is less than the magnitude of the relative velocity of the boat w.r.t the stationary observer. 

Solution

The correct options are
A Velocity of COM will be zero 
C The magnitude of relative velocity of the boat with respect to the walking man is greater than the magnitude of the relative velocity of the boat w.r.t. the stationary observer. 
Given,
mass of man M=(m1)=50 kg
mass of boat m=(m2)=300 kg

With respect to the stationary observer, man moves with a velocity v=2 m/s and assume boat moves with a velocity =v1 m/s.

As we know, there is no external force on the system. Hence, the velocity of COM is zero (Vcom=0)

To determine the velocity of the boat with respect to a stationary observer on land :-
Vcom=m1v+m2v1m1+m2=0
m1v+m2v1=0
50×2+300×v1=0
v1=13 m/s=0.33 m/s

The negative sign implies that boat is moving in a direction opposite to that of the walking man on the boat (for a stationary observer on land) 

To determine velocity of boat w.r.t walking man, we can find relative velocity as 
vbm=vbvm
where vbm= velocity of boat w.r.t walking man
vb= velocity of boat w.r.t. stationary observer =v1
vm= velocity of walking man w.r.t stationary observer =v
vbm=(13)(2)=73 m/s
=2.33 m/s

Hence magnitude of relative velocity of boat w.r.t the walking man is greater than the magnitude of the relative velocity of boat w.r.t the stationary observer. 
Option (a) and (c) are correct.

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