A catapult in a room?

Question

So, water balloons are launched from a catapult in a room with a ceiling of 3.9 m. If the initial velocity is 11 m/s, and the acceleration of gravity is 9.8 m/s, at what angle are the balloons launched to just graze the ceiling?

Answer 1

Vv=gt
h=(1/2) gt^2
t=sqrt(2h/g)
Vv= g sqrt(2h/g) or
Vv=sqrt(2gh)


V^2= Vv^2 + Vh^2
Vh= sqrt(V^2 - Vv^2)

Since Vv/Vh=tan(A)
The angle A is
A=arctan(Vv/Vh)
A= arcTan( sqrt(2gh)/sqrt(V^2 - Vv^2)=
A=arcTan( sqrt(2gh)/sqrt(V^2 - 2gh))=