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Answer :
Final answer:
The rocket will take 8 seconds to return to the ground.
Explanation:
The height h(t) of the rocket at time t is given by the equation h(t) = -16t^2 + 128t, where t is the time in seconds. To find the time it takes for the rocket to return to the ground, we need to find the value of t when h(t) = 0.
Setting h(t) = 0, we get:
-16t2 + 128t = 0
Factoring out -16t, we have:
-16t(t - 8) = 0
Setting each factor equal to zero, we find two possible values for t: t = 0 and t = 8. Since time cannot be negative, we discard t = 0.
Therefore, it will take the rocket 8 seconds to return to the ground.
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