Question

A bottle rocket is shot off a bridge into the stream below. The height of the rocket (in feet) above

Answer 1

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

h(t) = -16t² + 96t + 112

Answer:

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