A tennis ball is projected at an angle ∅ attains a range of R = 78m

Question

If the velocity is imparted to the ball by the racket is 30metre per second , calculate the angle ∅

Answer 1

Vertical problem
Vi = initial speed up = 30 sin ∅
v = Vi - g t = 30 sin ∅ - 9.81 t {if g = 9.81 m/s^2 on this planet}
h = 0 + Vi t - 4.5 t^2
at ground h = 0 so
0 = t ( 4.5 t -Vi)
so when it is at ground level again,
t = 30 sin ∅ / 4.5 = 6.67 sin ∅
now do the horizontal problem
u = 30 cos ∅ forever
78 = u t = 30 cos ∅ * 6.67 sin ∅ = 200 cos ∅ sin ∅
79 = 200 [ .5 sin 2 ∅ ]
solve for ∅

Answer 2

V