If a person shoots a basketball overhand from a position of 8 feet from the floor, then the path of the basketball through the hoop can be modeled by the parabola y = (-16x^2/0.434v^2) + 1.15x+8, where v is the velocity of the ball in ft/sec, y is the height of the hoop and x is the distance away from the hoop. If the basketball hoop is 10 feet high and located 17 feet away, what initial velocity v should the basketball have to go through the hoop?

Question

Mathematics

Ethan Ponce

9 March, 01:30

If a person shoots a basketball overhand from a position of 8 feet from the floor, then the path of the basketball through the hoop can be modeled by the parabola y = (-16x^2/0.434v^2) + 1.15x+8, where v is the velocity of the ball in ft/sec, y is the height of the hoop and x is the distance away from the hoop. If the basketball hoop is 10 feet high and located 17 feet away, what initial velocity v should the basketball have to go through the hoop?

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Nickolas Hayes · Answer 1

The ath of the basketball through the hoop can be modeled by the parabola y = (-16x^2/0.434v^2) + 1.15x+8, where v is the velocity of the ball in ft/sec, y is the height of the hoop and x is the distance away from the hoop. If the basketball hoop is 10 feet high and located 17 feet away then:

y = (-16x^2/0.434v^2) + 1.15x+8

10 = [-16 (17) ^2/0.434v^2] + 1.15 (17) + 8

v = 24.64 ft/s