Question

The rocket is launched from a cliff. The relationship between the height of the rocket,h, in feet, and the time since its launch,t, in seconds, can be represented by the following function:h(t)=-16t^2+80t+384a. Sketch the graph of the motion of the rocket b. When does the rocket hit the groundc. When does the rocket reach its maximum height d. What is the maximum height the rocket reaches e. At what height was the rocket launched

Answer 1

Given the function:

`h(t)=-16t^2+80t+384`

Which is The relationship between the height of the rocket,h, in feet, and the time since its launch,t, in seconds

a. Sketch the graph of the motion of the rocket?

The graph will be as shown in the following picture

b. When does the rocket hit the ground?

The rocket will hit the ground when h(t) = 0

So, from the graph, it will hit the ground at t = 8 seconds

c. When does the rocket reach its maximum height?

The maximum height will be at the point (2.5, 484)

so, the rocket will reach the maximum height at t = 5/2 = 2.5 seconds

d. What is the maximum height the rocket reaches?

As shown, The maximum height will be at the point (2.5, 484)

So, the maximum height = 484 feet

e. At what height was the rocket launched?

The rocket launched at t = 0

so, the rocket launched from the point (0, 384)