Physics projectile problem - finding vertical range using the horizontal range

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SUMMARY

The discussion focuses on calculating the maximum vertical height a baseball player can achieve when throwing a ball with a horizontal range of 54 meters. The relevant physics equations include d = Vo*t + 0.5*a*t^2, where vertical acceleration (a) is 9.8 m/s² and initial vertical velocity (Vyo) is 0 m/s. The user attempts to graph a parabola to find the vertical height but encounters confusion due to insufficient information about the initial velocity or angle of projection. The key takeaway is that the optimal angle for maximum range is 45 degrees, which should be considered for accurate calculations.

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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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