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The fireworks will use rockets launched from the top of a tower near the school. The top of the tower is 160 feet off the ground. The mechanism will launch the rockets so that they are initially rising at 92 feet per second.
The team members want the fireworks from each rocket to explode when the rocket is at the top of its trajectory.

They need to know how long it will take for the rocket to reach the top, so that they can set the timing mechanism. Also, in order to inform spectators of the best place to stand to see the display, they need to know how high the rockets will go.

The rockets will be aimed toward an empty field and shot at an angle of 65 degrees above the horizontal. The team members want to know how far the rockets will land from the base of the tower so they can fence off the area in advance. (Note: The field where the rockets will land is at the same level as the base of the tower.)
The height of the fireworks is given by the equation: h(t) = -16t2 + 92t + 160

The horizontal distance formula is: d(t) = 92t / tan 65

QUESTION: Use the given horizontal distance formula to find out how far the rocket lands from the original launch site. Also, 2. Write a clear statement off the questions the soccer team wants answered?

I already found the time it takes for the rocket to reach the ground: 7.149 seconds and I tried plugging this time in but I'm just not sure if I'm right. Please help?

Thank you!!!

The rocket hits the ground when the height is 0

0 = = -16t^2 + 92t + 160

Use the quadratic formula to solve for t and reject the negative root

t = 7.149 seconds is correct

Put this value in for t in the horizontal distance formula

d(t) = 92t / tan 65

d(7.149) = (92)(7.149)/ 2.146 = 306.481 ft

They want to know how far the rocket will land from the base .
The answer is 306.481 ft

They want to know how long it takes for the rocket to reach its maximum height.

Thus , you need to find the value for t that makes -16t^2 + 92t + 160 a maximum.

(you have not asked me to answer this question)

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I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.


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