Question

A batter hits a ball with an initial velocity v0 of 100 feet per second at an angle theta to the horizontal. An outfielder catches the ball 200 feet from home plate. Find theta if the range of a projectile is given by the formula R=1/32v0 squared times sin 2 theta.
Note: the zero by the v is supposed to be a little subscript zero.

Answer 1

R = (1/32) Vo^2 sin 2 T
hope I have that right. I do not do that problem that way.
200 = (1/32) (10,000) sin 2 T
so
sin 2 T = .64
2 T = sin^-1 .64 = 39.8 deg
so
T = 19.9 degrees

Answer 2

Yes
v = Vo sin T - 32 t
at top the distance = half range and v =0
t = (Vo sin T)/32
so full range
t full range = (2 Vo/32) sin T
so
Range = Vo cos T (2 Vo/32) sin T
Range = (1/32) Vo^2 (2 cos T sin T)
BUT
2 cos T sin T = sin (2 T)
TRIG IDENTITY
so
Range = (1/32) Vo^2 sin(2T)
so I believe you