Find the ratio of velcities of block A and B at the instant as shown

Explanation

Total length of string
`L=2(a^(2)+h^(2))^(1//2)+y`
Differentiating w.r.t. time t, we get
`(dL)/(dt)=2xx(1)/(2)(a^(2)+h^(2))^(-(1)/(2))(0+2h(dh)/(dt))+(dy)/(dt)`
`0=2(h)/(sqrt(a^(2)+h^(2)))(-v_(A))+v_(B)`
`0=-2v_(A)costheta+v_(B)`
`(v_(A))/(v_(B))=(1)/(2costheta)`