Question

A 2.0-m-tall basketball player is standing on the floor a distance d from the basket, as
shown in the figure below. He shoots the ball at an angle of 40.0o
above the horizontal
with a speed of 10.67 m/s and makes the shot. The height of the basket is 3.05 m. What
is d?

Answer 1

using x instead of d,

y = 2.0 + x tanθ - g/(2 (v cosθ)^2) x^2
v cosθ = 10.67 cos 40° = 8.17
tan40° = 0.84

so,

y = 2.0 + .84x - .073 x^2
Now, where does y=3.05?

2.0 + .84x - .073 x^2
x = 10.08