Box asked in Science & MathematicsPhysics · 4 weeks ago

The free throw line in basketball is 4.57 m (15 ft) from the basket, which is 3.05 m (10 ft) above the floor. A player standing on the free throw line throws the ball with an initial speed of 7.7 m/s, releasing it at a height of 2.3 m (7.5 ft) 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 it allows for a larger margin of error. Explicitly show how you follow the steps involved in solving projectile motion problems.

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• NCS
Lv 7
4 weeks ago

I'd use the trajectory equation

y = h + x·tanΘ - g·x² / (2v²·cos²Θ)

which can be rearranged after some trig substitutions to be

y = (h - gx²/2v²) + x*tanΘ - (gx²/2v²)tan²Θ

set k = gx² / 2v² = 9.8*4.57² / 2*7.7² = 1.726

let z = tanΘ

we have

3.05 = (2.3 - 1.726) + 4.57z - 1.726z²

The larger root (corresponding to the larger angle) is

z = tanΘ = 1.888

Θ = 62º