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) = 1/125d^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 will be 0. We can set h(d) = 0 and solve for d:

0 = 1/125d^2 + d
Multiplying both sides by 125d^2, we get:
0 = d^2 + 125d

Now we can use the zero product property and set each factor equal to zero:

d^2 = 0 or d + 125 = 0

The first solution d = 0 doesn't make sense in this context because it would mean the ball didn't travel any distance horizontally. Therefore, we use the second solution:

d + 125 = 0
d = -125

This negative value doesn't make sense either, so we conclude that the ball lands on the ground at a horizontal distance of 125 meters from where it was hit.