Question

a body is projected at an elevation alpha with a velocity of 9.8m/s in what time Wii be direction of motion be alpha/2?

Answer 1

just use your equation of motion, and find when its slope (derivative) is tan(alpha/2).

Answer 2

recall that

x = vcosθ t
y = vsinθ t - g/2 t^2

dy/dx = dy/dt / dx/dt
= (vcosθ - gt)/(-vsinθ)
-cotθ + g/(vsinθ) t

we want dy/dx = tan(θ/2) = (1-cosθ)/sinθ = 1 - cotθ

-cotθ + g/(vsinθ) t = 1 - cotθ
t = vsinθ/g