Mike wants to make a free throw; he realizes that if the ball is exactly 20cm above the hoop as it hits the backboard at the top of its trajectory, it will go in. The free throw line is 4.5 m from the plane of the backboard and the hoop is 3 meters from the ground, Mike throws the ball at a height of 2 meters. What velocity does he need in order to hit the backboard 20 cm above the hoop.

1 answer

distance horizontal=4.5m

vertical path:
hf=hi+vi*sinTheta*t-4.9t^2
3.20=2+v*sinTheta*t-4.9t^2
horizonal path:
4.5=v*cosTheta*t

so you have three unknowns, v, theta, and t. There is not a unique solution.