A bottle rocket is shot off a bridge into the stream below. The height of the rocket (in feet) above the water is modeled by h (t) = -1662 +96t + 112, where t represents time (in seconds).

How many seconds will it take for the rocket to reach its maximum height?

seconds

What is the maximum height the rocket will reach?

feet

How many second will it take for the rocket to hit the water?

seconds

The correct model of the height of rocket above water is;

h(t) = -16t² + 96t + 112

time to reach max height = 3 seconds

h_max = 256 ft

Time to hit the water = 7 seconds

Step-by-step explanation:

We are given height of water above rocket;

h(t) = -16t² + 96t + 112

From labeling quadratic equations, we know that from the equation given, we have;

a = -16 and b = 96 and c = 112

To find the time to reach maximum height, we will use the vertex formula which is; -b/2a

t_max = -96/(2 × -16)

t_max = 3 seconds

Thus, maximum height will be at t = 3 secs

Thus;

h_max = h(3) = -16(3)² + 96(3) + 112

h_max = -144 + 288 + 112

h_max = 256 ft

Time for it to hit the water means that height is zero.

Thus;

-16t² + 96t + 112 = 0

From online quadratic formula, we have;

t = 7 seconds

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

x=6 and x=3

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