Geometry and Basketball

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Ball is released at the same height as the hoop The combinations of θ and V that would allow the ball to land at a designated position will be plotted out as a curve on a graph with the shot speed V as the horizontal axis and the angle θ as the vertical axis. Values of X set equal to 13.25 feet, 14 feet, and 14.75 feet. In the figure given on the next page, ÿ The right curve is for ball to pass through front rim. ÿ Center curve is for the ball to pass through the centre of hoop. ÿ Left curve is for the ball to land at the back rim. The crescent area present between the left and the right curves gives the combinations of θ and V that is sufficient for the ball to land between the front and back of the rim, which is rhe prerequisite for a good shot. It is difficult for players to have perfect control over the speed of the ball and angle of release, with which they shoot the ball. To have a high percentage of success of baskets ( or good shots) certainly it is good to shoot the ball targeting the zone where the area between the left and right curve is the largest. From the figure, the largest acceptance area comes out to be at the front end of the shape so formed (crescent) with θ equal to 45°. The ball is released Y feet lower than the hoop. Here too, we will try to plot the curve on the graph with shot speed V as the horizontal axis and the angle θ as the vertical axis. The largest acceptance area again, comes out to be at the front end of the shape
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