The solution has been excellently provided by @aankurverma
Given,
v0 = v0 j
a = k(v x A)
A = (-c/y) k
Now,
a = (kc/y)vx j - (kc/y)vy i
v y.dv y/dy = (kc/y)v x = (kc/y)  (v 2 - v y2) At maximum height, y m, the y component of velocity is zero.  0 [vy/ (v2 - vy2)]dvy = kc y0ym (1/y)dy
Integrating you should get the answer.
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