Question

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Answer 1

9 seconds

Explanation:

The height of the rocket is given by the function h(t) = -16t² + 144t, where t represents the time in seconds after launch.

The rocket will hit the ground when its height is zero, so when h(t) = 0.

Set the function h(t) to zero:

`-16t^2+144t=0`

Factor out the common term -16t:

`-16t(t-9)=0`

Apply the Zero Product Property by setting each factor equal to zero and solving for t:

`\implies -16t=0 \implies t=0`

`\implies t-9=0 \implies t=9`

When t = 0, the rocket is launched.

Therefore, the rocket hits the ground at 9 seconds.