if a rocket is launched straight up into the air with an initial velocity of 112 feet per second, it's height after t seconds is given by the formula h = 112t - 16t, where x represents the height of the rocket in feet:

A. When will the rocket reach it's maximum height

B. What is the maximum height?

(Please explain how to do the problem but if you can't that's ok. I can work with a link that will show me how to do it. Thank you for answering.)

NOT AM ACTUAL ANSWER. THIS IS BY THE SAME PERSON. IMPORTANT SIDE NOTE: the -16t is squared.

your equation is not correct, should be

h = 112t - 16t^2

This is a parabola opening downwards
You have to find the vertex, and A and B can be answered at that point
hint: the t of the vertex is -b/(2a)
plug that back into the equation to get h, the maximum

let me know what you get.

When the rocket will reach max height:

1/14 seconds

Maximum height: 7.918... Feet

BY SAME PERSON WHO ASKED QUESTION

To find the maximum height of the rocket and the time it takes to reach it, we can use the concept of quadratic equations.

First, let's rewrite the formula for the height of the rocket as a quadratic equation:

h = 112t - 16t^2

In this equation, the coefficient of t^2 term is negative (-16), indicating a downward facing parabola. The maximum point of the parabola represents the highest point reached by the rocket.

To find the time at which the rocket reaches its maximum height, we need to determine the value of t when the velocity (rate of change of height with respect to time) is zero.

The velocity of the rocket is given by the derivative of the height equation with respect to time:

v(t) = d(h)/dt = 112 - 32t

Setting the velocity equal to zero and solving for t:

112 - 32t = 0
32t = 112
t = 112/32
t = 3.5 seconds

Therefore, the rocket reaches its maximum height at 3.5 seconds.

To find the maximum height, substitute this value of t back into the original height equation:

h = 112t - 16t^2
h = 112 * 3.5 - 16 * (3.5)^2
h = 392 - 196
h = 196 feet

Thus, the maximum height reached by the rocket is 196 feet.