Question

A ball is hit from the ground. When the ball has traveled a horizontal distance of d meters, its height, h, in meters, can be modeled by the function h(d) = 1/125 d^2 + d

What is the horizontal distance from the point where the ball is hit to the point where the ball lands on the ground?

Answer 1

When the ball lands on the ground, its height is 0. So we need to solve for d in the equation:

h(d) = 0

0 = 1/125 d^2 + d

Multiplying both sides by 125 to get rid of the fraction:

0 = d^2 + 125d

Now we can use the quadratic formula:

d = [-b ± √(b^2 - 4ac)] / 2a

where a = 1, b = 125, and c = 0.

d = [-125 ± √(125^2 - 4(1)(0))] / 2(1)

d = [-125 ± √(15625)] / 2

d = [-125 ± 125] / 2

We can discard the negative solution, since the distance can't be negative:

d = 0 or d = -125

So the horizontal distance from the point where the ball is hit to the point where the ball lands on the ground is 125 meters.