Any help here would be greatly appreciated, especially answering the initial vel

Question

Any help here would be greatly appreciated, especially answering the initial velocity. If I can get the initial velocity I should be able to do the rest easily.

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A basketball player would like to know an exact velocity and angle she should shoot a ball for her free throw to score a perfect goal. Assume that the front of the rim is 4 meters from the shooter. and the center of the basket is at 4.25 meters from her. The height of the rim is 1 meter up from where the ball is launched. The center of the ball must clear the front edge of the rim by 0.125 meters so that the ball swishes through the basket.

Explanation / Answer

let t is the time taken by centre to reach .125 m to rim, t" is time taken by centre to reach centre of the rim along vertically 1.125=u*t+4.9*t^2, 1=u*t"-4.9*t"^2 horizontally 4=v*t , 4.25=v*t" eliminating t and t" from the equations we have 1.125=u*4/v - 4.9*16/v^2 and 1=u*4.25/v-4.9*18/v^2 solving we get v=2.02 and u=10.75 that means he should throw witha velocity of sqrt(2.02^2+10.75^2)=10.94 m/sec and an angle of tan^-(2.02/10.75)=10.66 degrees to the horizontal.

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