Question

When a basketball player shoots a foul shot, the ball follows a parabolic arc. This arc depends on both the angle and velocity with which the basketball is released. Two equations are given below. The player's feet are at the origin. -16x2 Equation 1: y 0.434v2 + 1.15x +8 Equation 2: y72.75x +3 -16x2 0.117v2 For each equation, if the basketball hoop is 10 feet high and located 15 feet away, find the initial velocity v. Using the appropriate v, produce one professional-looking graph that shows both equations on a reasonable window. Include the location of the hoop. Determine which equation represents an overhand foul shot and which represents an underhand foul shot. From what height is each released? What is the maximum height of the basketball in each case?

Answer 1

Equation - 1 y = -16 x^2/0.434(23.32)^2 + 1.15x + 8 y = -0.06 x^2 + 1.15 x + 8 \r\n Equation - 2 y = -16x^2/0.117 v^2 + 2.75 x + 3 y = -0.15 x^2 + 2.75 x + 3 \r\n y = -0.06 x^2 + 1.15 x + 8 \r\n (a) Equation 1 - y = -16x^2/0.434 v^2 + 1.15 x + 8 y = 10 x = 15 10 = -16(15)^2/0.434 v^2 + 1.15(15) + 8 8294.93/v^2 = 15.25 v = 23.32 f/s \r\n Equation 2 y = -16x^2/0.117 v^2 + 2.75 x + 3 y = 10 x = 15 10 = -16(15)^2/0.117 v^2 + 2.75(15) + 3 30769.23/v^2 = 34.25 V = 29.97 f/s
Question 3- The maximim height in 1st case is 13.5 f and in 2nd case is 15.6 f