Question

Figure shows a Yacht of mass 400 kg with three decks. When the engine of Yacht is off, four men A, B, C and D ($m_A=100kg,m_B=120kg,m_C$ and $m_D=100kg$) started running on different decks with constant horizontal velocities relative to yacht which are marked in figure. All the velocity vectors are collinear. Due to this, Yacht also started moving. What is the speed in m/s with which Yacht moves.

• A. $7m/s$ towards right
  
• B. $7m/s$ towards left
  
• C. $14m/s$ towards left
• D. $14m/s$ towards right
  
• E. does not move
  

Answer 1

Answer: (B)

$7m/s$ towards left

There is no external force acting on the system in horizontal direction.
Initially, the com mass of the system ( yatch plus four men ) was at rest. Subsequently, it will remain at rest.
Let the yatch moves towards right with velocity v.
Velocity of four men will be $v+40,v+20,v+10,v-16$
Total momentum is $400v+100(v+40)+120(v+20)+80(v+10)+100(v-16)=0$
$\Rightarrow 800v=-5600$
$\therefore v=-7m/s$
The yatch moves towards left with velocity 7 m/s.