Question

The velocities of A and B are marked in the figure. Find the velocity of block C (assume that the pulleys are ideal and string inextensible)

Answer 1

From the figure-

$l_1+l_2+l_3+l_4=constant$

if block B moved by $X_1$ and block A moved by $X_2$ then - (block C moves down by $X_4$ and $l_3$ remain same)

Now - $(l_1-(X_1-X_2\left)\right)+l_2-(X_1-X_2)+l_3+(l_4+X_4)=(l_1+l_2+l_3+l_4)$

$(X_1+X_2)$ taken by the relative change in the position

$(l_1+l_2-2(X_1-X_2\left)\right)+l_3+l_4+x_4=l_1+l_2+l_3+l_4$

$\to -2(X_1-X_2)=-X_4$

thus $X_4=2(X_1-X_2)$

derivate with respect to time :-

$\frac{d{x}_4}{dt}=2(\frac{d{x}_1}{dt}-\frac{d{x}_2}{dt})$

$V_4+2(V_1-V_2)=2(3-1)=4m/s$

because - block 'c' is also in th contact with B.

so the net velocity of the block c:-

$\overrightarrow{V_c}=-3\hat{i}-4\hat{j}$

speed =$|\overrightarrow{V_c}|=\sqrt{3^2+4^2}=5m/s$