hi,

at any time ,

let the length of string between the wedge & pully(which is stationary ) = x2

 length of string between the block  & pully (to which it is hanged ) = x1

 length of string between the both pullys =  x2/ cos(90-θ)  = x2 / sinθ

since the length of strig would be const. so the sum of upper mentioned lenght would be const.

x1 + x2 + x2/ sinθ  = const.

d/dt x1  + d/dt x2  + d/dt ( x2/ sinθ  ) = 0

v1  - v2  - v2 /sin θ   -  x2 cosθ /sin^θ  (d/dt θ) =0 .............(1)

let the height of the wedge be l,then

 v1  - v2  - v2 /sin θ   + v2 cos^θ / sinθ   =0

v1- v2 - v2 /sinθ( 1 - cos^2θ ) = 0 

v1 -v2  - v2 sinθ =0

v1 = v2 (1 + sinθ )     (d )