MATH URGENT!!!!

posted by Melisa

With the given model: h=-0.045d^2+2d
where h is the height of the ball from the ground(in yards) and d is the horizontal distance of the ball(in yards) from its starting point.

A.)Pat is standing on the 17-yard line when the football passes over his head. How high up is the football at this point?

B.)The football is 8 yards above the ground when it passes over Billy. At what yard line is Billy standing when the football passes over his head?

  1. Jai

    for (a), we substitute 17 to d in the equation for the height,h:
    h = -0.045d^2 + 2d
    h = -0.045*(17^2) + 2(17)
    h = 20.995 yards

    for (b), we are given the height and we need to find the horizontal distance. substituting,
    h = -0.045d^2 + 2d
    8 = -0.045d^2 + 2d
    0 = -0.045d^2 + 2d - 8
    note that this is a quadratic equation and we can either factor it or use quadratic formula to solve for d,, here, let's just use quadratic formula:
    d = [-b +- sqrt(b^2 - 4ac)]/(2a)
    d = [-2 +- sqrt(2^2 - 4(-0.045)(-8))]/(2(-0.045))
    d = [-2 +- sqrt(2.56)]/(-0.09)
    d = [-2 +- 1.6]/(-0.09)
    d = 40 yards
    d = 4.44 yards
    note that there are two answers. for the 4.44 yards, the ball is going up, while for the 40 yards, the ball is already going down.

    hope this helps~ :)

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