well i have given a try & got a bit different answer..

 

as plane is smooth so friction absent.....hence no heat dissipated...

 

so applying energy conservation we get

 

1/2 m v^2 = work done by force F.(F = mg/2)

1/2 mv^2 = (mg/2)(s)(cosk)

 

solving we get

 

v = (gscosk)^1/2

also, k = as , so s = k/a putting  above we get

 

v = (gk/a.cosk)^1/2 -------ans..

 

plzz point out my mistake...