Question

I really need help with this assignment. I've got 1-3 done but the rest is confusing me can someone help??

Answer 1

Imagine you are a fountain designer and you need to know how different speed motors will affect the water’s projected height and time in the air. You have various motor speed options but need to choose the one that most closely meets the client’s height request of 690 feet. Your job is to determine which motor speed is the best choice. In all cases, you will use the projectile formula
y = –16x2 + vx + s, with starting height of 0 (s = 0).



Substitute the data provided for speed (v) and starting heights (s) into their proper positions in the formula
y = –16x2 + vx + s and write the equation corresponding with each motor in the space provided below.
Then identify the a, b, and c values for each where indicated. (6 points total, 2 points each)
The equation for motor A is:
a =
b =
c =

The equation for motor B is:
a =
b =
c =

The equation for motor C is:
a =
b =
c =

Use graphing technology to graph the equation for each motor. Set rounding to 5 places. Save a copy of each graph and paste them here or attach them to the assignment. If you are using GeoGebra, follow these instructions to find the vertex and x-intercepts. (15 points total, 5 points each graph)

Look at each motor's graph and find the vertex coordinates. Then report them below. (12 points total, 4 points each)
Motor A Vertex coordinates:

Motor B Vertex coordinates:

Motor C Vertex coordinates:

What is the range in height from the tallest fountain to the shortest fountain? Round to the nearest foot. (3 points)

What is the relationship between speed and height in the three graphs? (3 points)

Recall that your client has made a height request of 690 feet. Which motor brings you closest to that request? (1 point)

Ο Motor A Ο Motor B Ο Motor C

Now, in order to synchronize the neighboring fountain head to begin as soon as this one returns to the ground, you need to determine the time the water from this motor is in the air. (4 points)
Using your graphing tool, find the x-intercepts for the chosen motor.

Save a copy of this motor’s final graph and paste it here or attach it to the assignment.
How many seconds does it take for the water from this motor to return to the ground? (2 points)

When looking for the maximum height of the fountain, which part of the graph do you need to locate? (2 points)

When looking for the time the water is in the air, which part of the graph are you using? (2 points)