Question

The velocities of $A$ and $B$ are shown in the figure. Find the speed (in m/s) of block $C$. (Assume that the pulleys and string are ideal).

Answer 1

As the block A is moving towards block B with

$v_{AB}=v_A-v_B=1-3=-2m/s$

Thus A is moving at 2m/s towards right with respect to B.

When A moves a distance x the string loosens by 2x. Hence the speed of block C with respect to B is $4m/s$.

$v_{CB}=4m/s$

HENCE

$v_{CG}$ the velocity of C with respect to ground .

$v_{CG}=v_{CB}+v_{BG}=4m/s\left(down\right)+3m/s\left(left\right)$ (Vector addition)

hence,

$|v_{CG}|=5m/s$ (Triangle law of vector addition)