Projectile Launch Angle: What Could Be Causing My Arccos Computation Problem?

AI Thread Summary
The discussion focuses on the formulas used to calculate projectile launch angles when the target is at different elevations. It highlights the need for distinct calculations based on whether the target is lower or higher than the launch point. The correct formula for a higher target includes adjustments for height differences and uses the Arccos function. There is a suggestion that a missing parenthesis in the formula could lead to computation errors. The conversation concludes with an inquiry about the source of the computation problem related to the Arccos function.
dejavu333
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Homework Statement
velocity:20m/s we're on 5m, target is on 10m. What are the possible launching angles? The diatance is 40m
Air resistance can be neglected.
Relevant Equations
none
if the target is lower than me, the formula is below, but if it's higher as in the task, a whole different formula is required I think.
a = 9.8 * distance^2 / velocity^2
phi = Arctan(distance / height_diff)
angle_if_elevation = ( Arccos((a - height_diff) / Sqroot(height_diff^2) + distance^2)) + phi ) / 2
 
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Your left out an open paren, so:
angle_if_elevation = ( Arccos((a - height_diff) / Sqroot((height_diff^2) + distance^2)) + phi ) / 2

The same formulas are used - with the "height_diff" being negative.
But, you may not get results to your expectation.
My guess is that your arccos computation is giving you a problem.

What do you think is the source of that problem?

I think this is your graphic:
projectile-angle.png
 
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