The basketball player likes to release his foul shots with an initial speed uo =

Question

The basketball player likes to release his foul shots with an initial speed uo = 23. 5 ft/sec. What value(s) of the initial angle theta cause the ball to pass through the center of the rim? Neglect clearance considerations as the ball passes over the front portion of the rim.

Explanation / Answer

Horizontal distance = 23.5*cos(teta)*t = 13.75 =>t = (13.75/(23.5*cos(teta))) Vertical distance = (13.75 * Tan(teta)) - (0.5*32.174*((13.75/(23.5*cos(teta)))^2)) =>3 = 13.75Tan(teta)-5.507376075-5.507376075Tan(teta)^2 =>5.507376075Tan(teta)^2-13.75Tan(teta)+8.507376075 = 0 =>Tan(Teta) = 1.364916817, 1.131734911 =>teta = 53.771803, 48.53621279 Degrees

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