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A toy rocket is launched vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 96 feet per second. The height [tex]h[/tex], in feet, of the rocket above the ground at [tex]t[/tex] seconds after launch is given by the function:

\[ h = -16t^2 + 152t + 6 \]

How long will it take the rocket to reach its maximum height? What is the maximum height?

Answer :

In physics, we calculate the time for a rocket to reach its maximum height and determine the maximum height attained using the provided functions and formulas.

To determine the time it takes for the rocket to reach its maximum height: Calculate the time using the formula t = -b / (2a) where a, b are coefficients of the quadratic equation.

To find the maximum height: Substitute the time calculated into the height function to get the maximum height the rocket reaches.

For the given rocket: The time taken to reach the maximum height is 4.75 seconds, and the maximum height attained is 330 feet.

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Rewritten by : Barada