Calculating the Angle of a Projectile Fired for 3x Range Horizontally

AI Thread Summary
To determine the angle of a projectile fired for a horizontal range three times its maximum height, one must apply the equations of motion correctly. The horizontal range (x) is given by x = vx*t, while the vertical motion is described by y = -1/2g*t^2. The relationship between the range and height needs to be established using Newton's second law of motion for both horizontal and vertical components. The initial assumption of using arctan(1/3) is incorrect, as it does not account for the dynamics of projectile motion. A proper analysis will lead to the correct angle needed for the specified range-to-height ratio.
jesuslovesu
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A projectile is fired so that its horizontal range is 3 times its max height. What is the angle?

Well, I'm stumped because I thought if I just drew up a triangle and did
arctan(1/3), I would get the correct angle... apparently not.
 
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What are the equations of motion?
 
hmm

x = vx*t
y = -1/2g*t^2

I'm not really sure where to go, how the 1:3 would factor into anything.
 
jesuslovesu said:
hmm

x = vx*t
y = -1/2g*t^2

I'm not really sure where to go, how the 1:3 would factor into anything.
Your equation for y is incorrect.

Set up Newton's second law of motion for the system, both directions!
 

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