Algebra ll question

Question

A golf ball is hit from the ground, and it’s height can be modeled by the equation h(t)=-16t^2+128t were h(t) represents the height (in feet) of the ball t seconds after contact. What will the maximum height of the ball be? At what time will it reach its maximum height? Show work.

Answer 1

Using calculus, the velocity is -32t + 128. The maximum height occurs when the velocity is 0, so we have -32t + 128 = 0, and t = 4. The maximum height is then -16*16 + 128*4 = 256

To do it without calculus, recognize that the general equation for vertical motion is d = v_i *t - 1/2 * a *t^2. This applies when the initial velocity (v_i ) is up, and the acceleration of gravity (a) acts to reduce that velocity.

Our equation is: d = -16t^2 + 128t , so the initial velocity is 128 and a/2 = 16, so a = 32 ft/sec^2 (acceleration of gravity)

First, find the time using v = a*t. The golf ball is decelerating from 128 to zero, where a is 32. Therefore, t = 4.

Finally, find the distance by plugging in 4 for t in the original equation.

Answer 2

Elizabeth

Here you need to know the equation of the vertex -b/2a when your quadratic is in the standard form, which yours is. The vertex is the highest point of the parabola. In this case it is -128/-32 which is 4, that is the time, or the x coordinate. If you plug 4 in to the equation you get 256, the height in feet at time 4 seconds

All the best

Lori

Answer 3

This is a parabola that opens down, so it has a max at x = -b/2a (or t = -b/2a for this problem)

t = -128/[2(-16)] = 4

So when t = 4 it is at its highest.

That maximum height is found by finding h(4), the height with t=4 plugged into every t.

h(4) = -16(4)^2 + 128(4) = 256 feet.

Answer 4

Hi there! I'd love to help you out with this :)

WIth these types of problems, to find the maximum height, we have to find the vertex. FIrst we will find the x-coordinate using the equation:

x = -b / 2a Where -16 is a and 128 is b. Now plug in and simplify:

x = -128 / 2(-16) = -128 / -32 = 4

Now, to find the actually height, we need to plug 4 in for x in the original equation and solve:

-16(4)² + 128(4)

-16(16) + 512

-256 + 512

256

So the maximum height is 256 feet. I hope this explanation was thorough and answered all of your questions. If you have additional questions, please don't hesitate to reach out! Learn on :)