Question

Two blocks are connected by an inextensible string as shown. The pulley is fixed. If block A moves down with speed v, find the velocit of block B at instant.

Answer 1

Length of the string is constant
`L=sqrt(x^(2)+d^(2))+y=(x^(2)+d^(2))^(1//2)+y`
Differentiating w.r.t. time t, we get
`(dL)/(dt)=(1)/(2)(x^(2)+d^(2))^(-1//2)(2x(dx)/(dt)+0)+(dy)/(dt)`
`(dL)/(dt)=0` [as L and d are constant]
`(dx)/(dt)=-v_(B)` [ x is decreasing with time]
`(dy)/(dt)=v`
`0=-(xv_(B))/(sqrt(x^(2)+d^(2)))+v=-v_(B)cosalpha+v`
`v_(B)=(v)/(cosalpha)`
`v_(B)`: horizontal velocity of B
`v_(B)=cosalpha=v`
`v_(B)=(v)/(cosalpha)`