Solving Trajectory Problem with 2 Variables (V,A)

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SUMMARY

The discussion focuses on solving a trajectory problem involving two variables: muzzle velocity (V) and distance (X) for a projectile launched from a height of 44.1 meters at a 30-degree angle. The participants clarify that the original expression provided lacks an equation format and needs to be restructured to graph the relationship between V and X effectively. The correct approach involves using the time of flight and horizontal velocity components to derive the range, leading to the formulation of a function that expresses muzzle velocity as a function of range.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of quadratic equations and their applications in physics
  • Experience with graphing tools or software (e.g., Excel, TI-89)
NEXT STEPS
  • Learn how to derive the range of a projectile using time of flight and initial velocity components
  • Study the relationship between angle of projection and range in projectile motion
  • Explore the use of Excel for graphing mathematical functions and analyzing projectile trajectories
  • Investigate the correct application of trigonometric functions in physics equations
USEFUL FOR

Students in physics courses, educators teaching projectile motion, and anyone involved in modeling or analyzing trajectories in engineering or gaming applications.

  • #31
It looks like you are making a big mistake in your inputs, either the variables or the formula itself, probably the formula. I used Excel and here are a couple of benchmarks

v0 = 150 m/s, R = 2057 m
v0 = 300 m/s, R = 8023 m

I cannot help you any more. It is between you and your TI-89.
 
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  • #32
Alright, I've moved to a computer with excel. If anyone would mind helping me out here (sorry for the trouble).

=(500*Sin(30)+Sqrt(500^2*Sin(30)*Sin(30)+2(44.1)(9.8)/9.8))*500cos(30)

is what I put in and it spits back out at me that I am doing something wrong..
 
  • #33
First off you need to put asterisks to denote multiplication. This 2(44.1)(9 .8) won't work.
Secondly, you need to put the angle in radians, not degrees.
 
  • #34
Almost there... I got it to work but when I put in 300 for Velocity I got a number around 40,000.

=(300*SIN(0.5236)+SQRT(300^2*SIN( 0.5236)*SIN(0.5236)+2*(44.1)*(9.8))/9.8)*300*COS( 0.5236)

That is my formula.
 
  • #35
Well, I do hope I can get a response quick before my school's library closes. If not Thanks for your help.
 
  • #36
Sciencerob said:
Almost there... I got it to work but when I put in 300 for Velocity I got a number around 40,000.

=(300*SIN(0.5236)+SQRT(300^2*SIN( 0.5236)*SIN(0.5236)+2*(44.1)*(9.8))/9.8)*300*COS( 0.5236)

That is my formula.
You put this 9.8 in the wrong place. It should divide everything not just the radical.
 

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