Calculating the Angle for a Basketball Free Throw: A 2D Motion Problem

[johnnyscans]

1. Problem is a basketball player shooting a free throw. We know that the free throw line is 4.57 m from the basket, which is 3.05 m above the floor. A player standing on the free throw line throws the ball with an initial speed of 7.15 m/s, releasing it at a height of 2.44 m above the floor. At what angle must the ball be thrown in order to hit the basket?



2. Not really sure where to go with it. I'm thinking that y = y0 + V0t + 1/2at^2 may be used (via solving the quadratic) but I'm really not sure. My professor touched on this type of problem really quickly in class so we haven't gone over it in detail.

 

[Delphi51]

Welcome to PF, Johnny.
These 2D questions usually require you to write an equation for the horizontal motion as well as one or two for the vertical part. You have the vertical equation. Is the horizontal motion accelerated or not? The answer will tell you which formula to use for the horizontal distance. Then you will have a system of two equations with two unknowns, angle and time.

Unfortunately it involves trigonometric functions so it will be difficult to solve. You might want to do it by trial and error. Guessing an angle, it will be easy to find the vertical position when the ball gets to the right horizontal position. If you do it on a spreadsheet, it will be easy to repeat the calc for many different angles until you find the one that works.