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

AI Thread Summary
The discussion centers on calculating the theoretical horizontal range of a rocket launched at a 79-degree angle from the vertical. The user calculated a maximum vertical height of 60 meters and a total flight time of 7 seconds but found a discrepancy between their theoretical horizontal distance of 93.1 meters and the experimental distance of 36.6 meters. They attempted to determine the rocket's horizontal velocity component and used various equations, including the tangent function, to relate vertical and horizontal components. Despite deriving an initial vertical velocity of 68.6 m/s, the calculations did not align with the experimental results. The user seeks clarification on their approach and the equations used to reconcile these differences.
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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.

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