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.
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?
1 answer
1 answer