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?
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.
To find the horizontal distance from the point where the ball is hit to the point where the ball lands on the ground, we need to determine where the height (h) of the ball becomes zero (0).
Given the function h(d) = 1/125 d^2 + d, we can set h(d) = 0 and solve for d.
0 = 1/125 d^2 + d
Let's multiply through by 125 to get rid of the fraction:
0 = d^2 + 125d
Now, we have a quadratic equation. To solve it, we can factor or use the quadratic formula. In this case, it can be factored as follows:
0 = d(d + 125)
So, either d = 0 or d + 125 = 0.
Since the distance cannot be negative, we can disregard d + 125 = 0. Therefore, the only solution is d = 0.
This means that the horizontal distance from the point where the ball is hit to the point where the ball lands on the ground is 0 meters.