I'll give an example of how I solve for range and such with the given information:

**A ball is thrown from a height of 1.86 m, at a speed of 21 m/s and at an angle of elevation of 59.4o. How far from the person who threw it does the ball land?**

Range: Vxt

Vx: Vcos Theta

Vy: V sin Theta

The method in which I solve for t goes as follows:

Vy = 21 * sin59.4

Vy = 18.07

Maximum Height: v²= 2a(s) +existing height of 1.86

Maximum height: 18.07² /2(9.8) = s -> 16.66 + 1.86 = 18.52m

Total time: Time down + Time Up

s + 1.86 = 1/2at² + s = 1/2at²

18.52*2 / 9.8 = t² + 16.66 * 2/9.8 = t²

1.94 + 1.84 = 3.78s

R = V cos Theta * t

R = ~40.4 m

The problem I encounter is simply that I do not know how, using this method, or by any other really, to compute the angle or initial velocity if Total time is not a given already.

Say the equation was rearranged and said:

A person threw the ball at an initial rate of 21 m/s from a height 1.86. It hit the ground at 40.4m. What was the angle of projection?

Can anyone help show me how to work these backwards? Would be highly appreciated.