Physics projectile problem - finding vertical range using the horizontal range

AI Thread Summary
To determine the maximum vertical height a baseball player can achieve when throwing a ball with a horizontal range of 54 meters, the projectile motion equations must be applied. The vertical acceleration is 9.8 m/s², and the initial vertical velocity is zero. The horizontal distance indicates that the optimal angle for maximum range is 45 degrees, which can be used to calculate the initial velocity. The problem requires finding the time of flight and using it to compute the vertical height. Clarification on the optimal throwing angle and the relationship between horizontal and vertical components is essential for solving the problem effectively.
gchuchro
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Homework Statement



What is the maximum vertical height to which a baseball player can throw a ball if his maximum throwing range is 54 m?

vertical: a=9.8 m/s/s, Vyo=0 m/s, d=?, t=?
horizontal: d=54 m, a=0 m/s/s, Vxo=?, t=?

Homework Equations



d=Vo*t+.5*a*t^2

The Attempt at a Solution



Since Vo or theta was not given, I decided to graph a parabola who's derivative would be 9.8t...so on my calculator I graphed 4.9t^2. Since I know it traveled 54 meters horizontally, I thought the y value of the parabola when x=27 would be my answer..but it clearly was not.

Any ideas on how to approach this? I'm confused because of the few givens I have to work with.
 
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Hi gchuchro and welcome to PF!

Firstly a question from me: how would you throw a ball if you wanted to throw it furthest away?
 

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