What is the Theoretical Range of a Rocket at 79 Degrees?

[ABigFig]

Homework Statement

My rocket was angled at 79 degrees from the vertical,
I calculated its maximum vertical height to be 60 meters,
The total flight time was 7 seconds
Experimental horiz distance is 40 yds (should be 36.6 meters)

Homework Equations

This is part of my problem, I am not sold on which equation would be best to use, but I have tried using the following (explained in my attempt):

Vf=Vi+(g)(t)
V(avg)=d/t
tan(theta)=(Viy(initial - vertical direction)) / (Vix(initial - horizontal direction))
D=Vi(t)+(1/2)(at^2): which lead me to the following equation:
Dh(horiz dist)=(Vix)(t)

The Attempt at a Solution

I'm trying my best to explain this clearly, if you think you can help me but don't understand something I wrote, please ask and I'll try to clear it up, I'm really stuck:

My main mission has been to find the rockets horizontal velocity component during flight, since that stays constant, so I can multiply it by flight time and get my theoretical horizontal distance. Since I do not know the rocket's initial velocity (Vi) I tried breaking it up into horiz and vert components. While trying that, I used my calculated vertical distance of 60 m, but I realized that I can only get an average velocity out of that measurement, which doesn't seem to help me find horiz distance. Just as I wrote that last part, I thought of using the tangent function to relate my vertical height and first half of horizontal height, which didn't match my experimental horiz distance at all. Then I tried making another triangle to relate horiz and vert velocities with tangent. I used Vf=Vi+gt and solved for Viy(Vi vertical), since I would technically be using Vix for horizontal velocity, since it doesn't change. Vf would be 0 at the top of the arc, so I subtracted gt and found Viy=68.6 m/s. It seemed a it high, but I went with it. Then I went back to my triangle. my launch angle is 79 degrees, and the leg opposite angle I set to 68.6 m/s as Viy, and solved it for the leg adjacent to the angle, which would be my Vix. Vix came out as 13.3 m/s. This sounded good, since 79 degress from vertical is only a bit from straight up, so I figured Viy should be substantially larger than Vix. However, I multiplied my unchanging Vix by the total flight time of 7 seconds, and received a theoretical horiz range of 93.1 m. Way off from my experimental distance of 36.6 meters.

 

[ABigFig]

I'm not sure why the list repeated itself at the bottom, sorry!

 

[jmb88korean]

If you know the final distance in the y direction (60 meters), the acceleration(gravity), and the time, which is half time due to max height being at half the distance/time, you can find initial y velocity. Using this and the angle, find the intial x velocity.