An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t^2 + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?

(1) 128 (3) 8

(2) 64 (4) 4

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- Jan 18th 2007, 07:33 PMsymmetryFind k
An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t^2 + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?

(1) 128 (3) 8

(2) 64 (4) 4 - Jan 18th 2007, 07:37 PMtopsquark
- Jan 18th 2007, 07:41 PMsymmetryok
Derivative is a calculus word.

I am not asking calculus questions at this point in the study book.

Thanks anyway! - Jan 18th 2007, 07:54 PMtopsquark
All right. In that case we need to look at the height function a bit more carefully. It is an inverted parabola. The maximum height will be at the vertex of the parabola, which is on the axis of symmetry.

Given a parabola the axis of symmetry will be the line .

We have the parabola . We know that the location of the max height is the line t = 4, which is our axis of symmetry. So:

So

.

-Dan - Jan 20th 2007, 05:56 AMsymmetryok
Dan,

Thanks for breaking the question some other way.

I am not ready for calculus questions at this point in the course of my review for the June state test.

Thanks! - Jan 20th 2007, 10:32 AMCaptainBlack