The free throw line in basketball is 4.57 m (15 ft) from the basket, which is 3.

Question

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 7.80 m/s, releasing it at a height of 2.52 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 it allows for a larger margin of error.

____________° above the horizontal

Explanation / Answer

Use the trajectory equation: y = h + x·tan - g·x² / (2v²·cos²)
where y = final height = 3.05 m
and h = initial height = 2.52 m
and x = range = 4.57 m
and = launch angle = ???
and v = 7.80 m/s

3.05 = 2.52 + 4.57tan - 9.8(4.57)² / (2(7.8)²cos²)
0 = -0.53 + 4.57tan - 1.682 / cos²
but 1 / cos² = sec² = 1 + tan²
0 = -0.53 + 4.57tan - 1.682 - 1.682tan²
0 = -2.212 + 4.57tan - 1.682tan²
is quadratic in tan with roots at
tan = 0.630 = 32.2º smaller angle
and tan = 2.087 = 64.4º larger angle

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.