Question

The velocities of A and B shown in fig. Find the speed (in `ms^(-1)`) of block C. (Assume that the pulleys and string are ideal).

Answer 1

Correct Answer - `5m//s`
By constrained equaiton for length
`l_(1) +l_(2) +l_(3) +l_(4) =` constant
`(dl_(1))/(dt) +(dl_(2))/(dt) +(dl_(3))/(dt) +(dl_(4))/(dt) = 0 …(1)`
since `(dl_(1))/(dt) = (dl_(2))/(dt) = v_(A) = v_(B) = 1-3 =- 2m//s & (dl_(3))/(dt) =0`
putting the value in eq.(1)
`-2 +(-2) +0+(dl_(4))/(dt) = 0`
`{:((dl_(4))/(dT)=4m//s,,rArr,v_(CB)=4m//s,),(vecv_(CB)=vecv_(C)-vecv_(B),,rArr,vecv_(C)=vecv_(CB)+vecv_(B),):}`
`v_(C) = sqrt(v_(CB)^(2)+v_(B)^(2)) rArr v_(C) = sqrt(3^(2) +4^(2))`
`rArr v_(C) = 5m//s`