Question

Assuming the water resistance to be negligible, find the horizontal component of the force with which the man acted on the raft during the motion.

• A. $F=-\frac{2mM}{M+m}\frac{d{v}^{\prime }}{dt}$
• B. $F=\frac{2mM}{M+m}\frac{d{v}^{\prime }}{dt}$
• C. $F=\frac{mM}{M+m}\frac{d{v}^{\prime }}{dt}$
• D. $F=-\frac{mM}{M+m}\frac{d{v}^{\prime }}{dt}$

Answer 1

The correct option is D $F=-\frac{mM}{M+m}\frac{d{v}^{\prime }}{dt}$

Let the velocity of raft be $v$, the velocity of COM will be zero as there is zero external force on raft + man system.

$m_1{v}_1=m_2{v}_2$...(i)

Velocity of man actual is $v^{\prime }-v$.

Using equation (i)

$m(v^{\prime }-v)=Mv$

$v=\frac{m{v}^{\prime }}{m+M}$

The force on raft will be change in its momentum in time $dt$.

$F_{raft}=\frac{d}{dt}\left(Mv\right)$

$F_{raft}=\frac{mM}{m+M}\frac{d{v}^{\prime }}{dt}$