Solving Trajectory Problem with 2 Variables (V,A)

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Homework Help Overview

The discussion revolves around a trajectory problem involving a cannon fired at a 30-degree angle. Participants are attempting to derive a relationship between muzzle velocity and distance, using various equations and expressions related to projectile motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants are exploring how to graph a given expression involving velocity and time, questioning the validity of the expression as an equation. There are attempts to clarify the relationship between muzzle velocity, distance, and time of flight, with some participants suggesting different formulations and questioning assumptions about the variables involved.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to approach the problem. Some are suggesting methods to derive the range from muzzle velocity, while others are questioning the correctness of the expressions being used. There is a recognition of the need to clarify the definitions and relationships between the variables involved.

Contextual Notes

Participants are working with limited information, primarily the height of the cannon and the angle of projection. There is confusion regarding the use of certain variables and the formulation of equations, which may affect the ability to graph the desired relationship accurately.

  • #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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