Thread: Throwing a ball across a field problem.

1. Throwing a ball across a field problem.

A ball is thrown across a field. Its path is given by the equation
y = -0.005x^2 + x + 5
where:
y = height
x = horizontal distance

What is the max height reached by the ball?

2. Originally Posted by needhelp75
A ball is thrown across a field. Its path is given by the equation
y = -0.005x^2 + x + 5
where:
y = height
x = horizontal distance

What is the max height reached by the ball?
If you're familiar with calculus, find where $\displaystyle \frac{\,dy}{\,dx}=0$ and then plug that value into the original function to find the maximum height.

Otherwise, you can use the fact that the vertex of a parabola occurs at the point $\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)$

vertex of a parabola looks more familiar,
where do i go next?

4. Originally Posted by needhelp75
vertex of a parabola looks more familiar,
where do i go next?
$\displaystyle a=-0.005$ and $\displaystyle b=1$

In the point for the vertex, $\displaystyle f\left(-\frac{b}{2a}\right)$ would yield the maximum height.

Thus, $\displaystyle f\left(-\frac{1}{2(-.005)}\right)=f\left(\frac{1}{.01}\right)=f\left(1 00\right)=\dots$

confirmed?

horizontal distance = 100
vertical distance = 55

is this correct?

6. Originally Posted by needhelp75
confirmed?

horizontal distance = 100
vertical distance = 55

is this correct?