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If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 ft/s, its height \( h(t) \) after \( t \) seconds is given by the equation:

\[ h(t) = -16t^2 + 128t \]

How long will it take for the rocket to return to the ground?

Answer :

We set the equation h(t) = -16t² + 128t equal to zero and found two possible values for t: t = 0 and t = 8. Since time cannot be negative, we discard t = 0 and conclude that it will take 8 seconds for the rocket to return to the ground.

To find out how long it will take for the rocket to return to the ground, we need to determine when the height (h) becomes zero. We can do this by setting the equation h(t) = -16t² + 128t equal to zero and solving for t.

-16t² + 128t = 0

First, we can factor out a common factor of 16t:

16t(-t + 8) = 0

Now we have two factors: 16t = 0 and -t + 8 = 0.

From the first factor, we find that t = 0.

From the second factor, we find that -t + 8 = 0, which means t = 8.

So, the rocket will return to the ground after 8 seconds.

In summary, we set the equation h(t) = -16t² + 128t equal to zero and found two possible values for t: t = 0 and t = 8. Since time cannot be negative, we discard t = 0 and conclude that it will take 8 seconds for the rocket to return to the ground.

Learn more about common factor from the given link;

https://brainly.com/question/30961988

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