# Range Equation Limitation question

1. Sep 27, 2013

### astropi

1. The problem statement, all variables and given/known data
First off, this is NOT a homework problem. I do not need an actual "answer", but I do have a conceptual question. Here it is:

Consider a projectile motion problem such as a baseball being hit. Assume that it is hit and caught at the same height above the ground. In this instance, I believe that the range equation will NOT work. Why not? Most textbooks claim that the so-called range equation works as long as the launch height and final height are equal. However, in such an instance, the range equation fails to give the correct launch angle.

2. Relevant equations
$$R = v_o^2/g * sin (2*\Theta)$$

3. The attempt at a solution
N/A

Last edited: Sep 27, 2013
2. Sep 27, 2013

### nasu

In what way it will not work? What makes you believe this?

3. Sep 27, 2013

### Enigman

Why shouldn't it work?
The proof and hence the equation does not depend on the height as long as max Height is not so high that their are changes in g.
I think your confusion lies in the fact that the same range can be obtained from two different angles $\theta \ and \ \pi/2$
An interesting animation:https://www.youtube.com/watch?v=N0H-rv9XFHk

Last edited: Sep 27, 2013
4. Sep 27, 2013

### astropi

I figured it would work, and am uncertain why it does not, or where I made an error. For example, consider the following: R = 35 m, t = 3.2s, y_o = 1.4 m, v_o = 19 m/s with v_y = 16 and v_x = 11, therefore theta = 55 degrees (by the way these values are from an old exam). The range formula does not properly compute theta, unless I made a silly error in which case I would like it pointed out. Thank you!

5. Sep 27, 2013

### Enigman

You don't need the range formula for finding $\theta$.
Use the fact $v_y/v_x=tan(\theta)$
EDT-And the answer should be $55.49^o$

Last edited: Sep 27, 2013
6. Sep 27, 2013

### astropi

Yes, I know that, thank you. However, that is not my question. My question is: why does the range equation not give you the correct value for theta?

7. Sep 27, 2013

### Enigman

What did you take g as?

8. Sep 27, 2013

### Staff: Mentor

It does! But there are two possible angles that satisfy the equation, and your "solving" it returned only one of the two, corresponding to the principal value returned by the sin-1 function. To get the other value, a little trig is involved. Consider the following situation on the unit circle:

https://www.physicsforums.com/attachment.php?attachmentid=62240&stc=1&d=1380292338

Two angles, $\alpha$ and $\alpha '$ will yield the same value for sine. The definition of the range and domain of the inverse sine function means it returns only the angle in the first quadrant. It's up to you to determine what $\alpha '$ is from there, if $\alpha '$ is the angle you need.

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9. Sep 27, 2013

### nasu

What is the actual text of the problem?
How is R defined here? Does it say that the end point is at the same height as the initial point?
It looks over-determined.

And what Gneill said, for sure.

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