You are a serious basketball player and want to use physics to improve your free-throw shooting. Do an approximate calculation of the minimum speed the ball must have to travel from your hand to the basket in a successful free throw. You will have to estimate or find several of the quantities indicated in Figure P4.70, including the distance x from your hand to the basket, the height h of the ball when it leaves your hand, and the height y of the basket. Graph how the initial velocity changes as a function of launch angle to find the minimum initial speed of the ball and the particular launch angle.

Figure P4.70

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