In the system shown, the block A is moving down eith velocity `v_(1)` and C is moving up with velocity `v_(3)`. Express velocity of the block B in terms of velocities of the blocks a and C.

Explanation

The method requires assigning position coordinate to each of the system, there are four separately moving bodies and two strings. The moving bodies are the three blocks and pulley P. We assign position coordinates in the figure. The required constant equation for string connecting block A and pulley P is
`x_(1)+x_(p)=l_(1)` ...(i)
And the required constant equation for the other string is
`x_(2)+2x_(3)-2x_(p)=l_(2)` ...(ii)
Let the block B is moving down with velocity `v_(2)`
The velocities are defined as `" "v_(1)=overset(.)(x)_(1), v_(2)=overset(.)(x)_(2)`, and `v_(3)=-overset(.)(x)_(3)`
Differentiating terms of eq. (i) and (ii), eliminating `overset(.)(x)_(p)` and substituting above values of velocities, we have
`v_(2)=2(v_(3)-v_(1))`