Question

A particle is launched from point a with a horizontal speed u

Answer 1

I assume you need the time of flight of the object.

A condition to get the time of flight or the range is that

s[y]=0 in that it is at ground level

u = u[x] i + u[y] j = 30 cos 30 i + 30 sin 30 j ,, note u[y] = 30 sin 30 30/2=15 m/s

Back to s[y] =0

s[y] = u[y] . t - [1/2].gt^2 =0 on landing

Then t = 2 u[y]/g = 2[15]/g =3secs = time of flight, if g=10

(max)s[x] = Range =R = u[x] . t = 30 cos 30 [3] = 45 sq rt 3