Explanation

`:'` Block A is moving with velocity `8 ms^(-1)`.
` :.` velocity of every point on the string must be `8m//s` along the string.
The real velocity of B is vB. Then the string will not break only when the compoent of `v_B` along string is `8 m//s.`
`implies V_(B) cos 37^(@) = 8 implies V_(B) = 8/(cos 37^@) = 10m//"sec"`