Projectile motion max height problem

AI Thread Summary
A projectile launched from ground level at 48.7 m/s needs to be analyzed to find the launch angle where its maximum height equals its horizontal range. The key equations involve horizontal and vertical components of motion, specifically Vocos(angle) for horizontal velocity and Vosin(angle) for vertical velocity. To solve the problem, both horizontal and vertical motion equations must be utilized, as they involve unknown time, initial velocity, and angle. The discussion emphasizes using a systematic approach to tackle projectile motion questions. Understanding these principles is essential for solving similar problems effectively.
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Homework Statement



A projectile is launched from ground level with an initial speed of 48.7 m/s. Find the launch angle (the angle the initial velocity vector is above the horizontal) such that the maximum height of the projectile is equal to its horizontal range. (Ignore any effects due to air resistance.)

Homework Equations



Vocos(angle)=Vx
Vosin(angle)=Vy


The Attempt at a Solution


(X, 0) and (X/2, Ymax)
 
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In my experience you can always solve these projectile motion questions with the high school method. Write x = vt for the horizontal part,
Vy = Viy + at AND y = Viy*t - ½at² for the vertical part.
In this problem you need all three equations because you have unknown t, Vi and the angle. Give it a try!
 

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