The basketball player HELP-Isaac Physics

So for Part D, the question asks
A basketball player wants to calculate the angle θ (measured from the horizontal) at which she needs to shoot a ball (of radius a) in order to score without the ball touching the rim. She would also like to know how long the ball is in the air. The basket (of radius 2a) is a height b above the ground, having its far side a distance l away from the centre of the ball. She throws the ball with its centre at a height h with an initial speed u.

Determine the speed at which the ball must be thrown in order to pass through the hoop at this shallowest angle you have calculated, in terms of g, l and a, when the ball is released from a height h=b.

Considering that my shallowest angle was given by sin(phi) == (1)/(2), I calculated t given that there was no displacement in the horizontal direction, given that the ball must travel a distance of (l-a), and the using projectile motion, I got that u was given by sqrt((2*sqrt(3) * (l - a) * g)/(3)). However this is wrong. Can someone please help??

Reply 1

mosaurlodon

Does this previous post about this question help?
https://www.thestudentroom.co.uk/showthread.php?t=6587488
edit: nevermind you're very close to the answer
think about whether the horizontal displacement is actually l - a, with the reminder that the centre of the ball needs to pass through the center of the hoop - draw a diagram if you need to.
hope that helps
I actually remember struggling on part c of this question I couldnt figure it out until I saw someones diagram