Projectile angle and maximum height

AI Thread Summary
To determine the projection angle at which the range of a projectile equals its maximum height, one must analyze the equations governing projectile motion. The maximum height occurs when the vertical velocity component is zero, while the range is calculated using the initial velocity and the sine of the angle. The discussion emphasizes solving for maximum height and equating it to the range without relying on double angle identities. Participants suggest focusing on the components of velocity and maintaining clarity in calculations. Ultimately, understanding the relationship between these two aspects is crucial for solving the problem effectively.
ThomasMagnus
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At what projection angle will the range of a projectile equal its maximum height?


I am having a lot of trouble with this one. Is there any way to solve this question without using double angle identities?

I know that this should be the first step:

Max height when Vy=o
Vfy2=Voy2 + 2(a)(dy)

0=(Vo2 + 2(a)(d)

Range= Vo2 sin2(theta)/g


I'm stuck here. Can anyone help me?

Thanks!
 
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What's wrong with double angle identities? They can always be undone. What does sin(2θ) become?

You're on the right track. Solve for the maximum height of the trajectory and set it equal to the range. Be sure to keep track of what's the total velocity and what are components.
 

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