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The rocket will be in the air for \( \frac{3}{4} \) seconds, or 0.75 seconds, before it returns to the ground.

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Here are some related questions to expand your understanding:

1. What does the coefficient \(-16\) represent in the equation?
2. How would the equation change if the initial velocity were increased?
3. How can you calculate the maximum height reached by the rocket?
4. What role does gravity play in this problem?
5. How can we model more complex vertical motions using differential equations?

**Tip:** When solving quadratic equations like this, always consider the physical context. For instance, the solution \( t = 0 \) refers to the moment the rocket is launched.

A model rocket is launched vertically upward with an initial velocity of 12 ft/s. The height of the rocket in feet after t seconds is given by s(t) = -16t^2 + 12t. Determine how long the rocket is in the air. Enter an exact answer.

Find out how long a model rocket stays in the air by solving the quadratic equation s(t) = -16t^2 + 12t. This detailed guide walks you through the key algebraic concepts and formulas needed to solve the problem. Perfect for students in Grades 9-10.

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