Projectile Motion: Solve Theta/Initial Velocity?

I have an array of dynamics problems that I can't figure out to save my life, any help would be much appreciated. The most basic problem is a projectile is launched at an angle theta and initial velocity and lands 126ft away after 3.6s (lands at the same elevation). Find theta and initial velocity.


What I've been trying to do is use:

x = x0 + V0x * t and y = y0 + V0y * t + a / 2 * t^2

I then use cos theta and sin theta multiplied by V substituted into their corresponding spots for V0x and V0y. If I punch in the variables for those equations and try to do them simultaneously solving for theta and V0 I don't get a correct answer, let alone corresponding to what the book says the answer is.

I've looked up stuff online, none of the examples in the book has to solve for theta, and no videos really help. I don't get why those two equations together shouldn't work, let alone what WOULD work. Thanks for any help again.

The time of flight was 3.6s, so you can solve for V0y immediately.

0 = 0 + v0y t - 4.9m/s^2 t^2
4.9m/s^2 t^2 = v0y t
4.9m/s^2 3.6s = v0y
17.66m/s = V0y

And again for V0x
38.4m = 0 + V0x 3.6s
38.4m / 3.6s = V0x
10.67m/s = V0x

Since you have both x and y components, you can solve for theta and speed. This is the same as converting rectangular coordinates to polar coordinates.

tan(theta) = y/x
theta = tan^-1(y/x)
theta = tan^-1(17.66/10.67)
theta = tan^-1(1.66)
theta = 58.9 degrees above horizontal.

V0^2 = (V0x^2 + V0y^2)
V0^2 = (17.66m/s)^2 + (10.67m/s)^2
V0^2 = 425.6m^2/s^2
V0 = 20.6m/s