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 7.20 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 it allows for a larger margin of error.

___________ ° above the horizontal

Explanation / Answer

x = 4.57m

y = 3.05m

h = 2.44m

v = 7.20m/sec

theta = ?

y = h +x*tan(theta) - (1/2)*g*x^2/{v* cos(theta)}^2

3.05 = 2.44 + 4.57* tan(theta) -(1/2)*g* 4.57^2/{7.20* cos(theta)}^2

0.61 = 4.57*tan(theta) - 1.97* {sec(theta)}^2

1.97[ 1 + {tan(theta)}^2 - 4.57* tan(theta) + 0.61 = 0

1.97* {tan(theta)}^2 -4.57*tan(theta) + 2.58 = 0

tan(theta) = 0.97 & 1.35

taking larger initial angle tan(theta) = 1.35

theta = 53.45 degree

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