Finding initial velocity given max height and distance only

AI Thread Summary
To find the initial velocity of a golf ball that reaches a maximum height of 20 m and lands 130 m away, the angle of projection is calculated to be 31.6 degrees. The user attempts to use the horizontal and vertical motion equations but struggles to isolate the initial velocity. There is a suggestion that the problem may be more straightforward than it seems. Clarification is sought on how the angle of 31.6 degrees was determined. The discussion emphasizes the need for a clearer method to solve for initial velocity without overcomplicating the calculations.
dane811
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Homework Statement



A golfer hits a ball, giving it a maximum height of 20 m. If the ball lands 130 m away at the level from which he hit it, what was its initial velocity? (Neglect air resistance)

Homework Equations





The Attempt at a Solution



I found the angle to be 31.6, so I tried vi cos 31.6 = 130 /(1/2)((-vi sin 31.6)/-9.81), but I'm not seeing how to solve for initial velocity. There has to be an easier way to do this, and I'm convinced I'm making it more complicated than it really is!

Any help would be appreciated!
 
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How do you get the angle to be 31.6°?
 
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