Question

The free-throw line in basketball is 4.57 m from the basket, which is 3.05 mabove 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 above the horizontal must the ball be thrown to exactly hit the basket?

Note that most players will use a large initial angle rather than a flat shot because itallows for a larger margin of error.

Answer 1

$x=v_x t,$

$y=y_0+v_yt-\frac{gt^2}2,$

$1.54\tan^2\alpha-4.57\tan\alpha+2.15=0,$

$\alpha=67.2°.$