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Question
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 65º

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?

The numbers in the answer I used Excel to find.
The answers have been made to have two places past the decimal,
though rounding to 0 places would be good enough
since gravity is rounded to 0 places.

Using the secant method of root-finding, I got 7.148830249,
which is the same as yours with a few more digits accuracy.

To find the height, note that the velocity is -32t + 92.
The maximum height would be when the velocity is 0.
That gives us -32t + 92 = 0, or 32t = 92.
Dividing both sides by 32 gives t = 92/32 = 23/8 = 2.875.

Putting t = 2.875 back in the height equation gives 1169/4 = 292.25.

If the horizontal distance is 92t / tan 65º,
using the impact time as t = 7.149 gives 306.69 feet.

Volunteer

#### Scott A Wilson

##### Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

##### Experience

Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.