Abrar Alali

Maitha AlMheiri

Sara Fawzi

Sara Al Ali

Elyazya Abdulaziz

The slide

This ride is located in the kiddie section! The height of the rider above ground, h yards, after t seconds can be modeled by the function:

h(t)=-0.5t+40

Let. h(t)=0

0=-0.5t+40

-40=-0.5t

t=80 sec

The little Drop

On this ride, for some period of time, the rider dips below the ground level. The height of the rider after (t) seconds can be modeled by the function:

h(t)=4t^-44t+96

What is the starting height of this ride?

Let (t)=0 seconds

h(t)=4t^2-44t+96

h(0)=4(0)^2-44(0)+96

h(0)=

96 meters

**Roller coaster**

Thank you!

How long does the ride last?

Change the numbers so that the ride starts

higher and drops faster.

h(t)=-0.5t+40

h(t)=-3(t)+80

Now how long does the ride last, based on the changes in part b?

h(t)=-4(t)+80

0=-4(t)+80

-80=-4t

t=20 sec

How long is the rider below the ground?

h(t)=4t^2-44t+96

=(t-3)(t-8)

t1=3 t2=8

8-3=

5 seconds

If the ride lasts a total of 10 seconds, what is the height of the exit gate?

t = 10 sec

h(t)=4(t)^2-44(t)+96

h(10)=4(10)^2-44(10)+96

=56m

The Scream

This ride lasts for 8 seconds. The height of the rider can be modeled by the function:

h(t)=9-6t^2+12t)(t^2-12t+32)

At which height does this ride begin?

let t = 0 seconds

h(t)=(-6t^2+12t)(t^2-12t+32)

h(0)=(-6(0)^2+12(0))((0)^2-12(0)+32)

= 0 x 32

= 0 meters

At what height does this ride end?

ride last 8 seconds so t = 8

h(t)=(-6t^2+12t)(t^2-12t+32)

h(0)=(-6(8)^2+12(8))((8)^2-12(8)+32)

= -288 x 0

= 0 meters

At what height is the ride after 5 seconds?

t = 5

h(t)=(-6t^2+12t)(t^2-12t+32)

h(5)=(-6(5)^2+12(5))((5)^2-12(5)+32)

= -90 x -3

= 270 meters

At what time(s) does the ride hit ground level?

Graph the function

let the function h(t) = 0

h(0)=(-6t^2+12t)(t^2-12t+32)

0=-6t^2+12t

0=(t-2)(t+0)

t1 = 2 , t2= 0

0=t^2-12t+32

0=(t-8)(t-4)

t1 = 8 , t2 = 4

graph the ride and label on the axis

calculate the period

between 2 sec and 4 sec

total period = 4-2

= 2 seconds

The Design

A roller coaster can be based on mathematical functions, but they are more likely to be made up of pieces, each of which is a different mathematical function. This allows much more flexibility. Use piecewise functions to design your own roller coaster. Include a graph of the roller coaster.

a. Each of the pieces are connected to each other.

Once you have decided on a design of your roller coaster and have graphed it answer the following questions using the graph and the function.

a. What is its starting height?

2 meter

b. How long does the ride last?

2= 256-16t2

2-256 = -16 t2

-254/-16 =-16 t2 /16

t2 = =15.875

t= -3.98 sec.

c. What is its ending height?

h= 256-16(-3.98)2

h= 2.5536 meter

2.5536 = 256-16t

d. Approximate how long it takes to reach its highest point?

7=256-16t2

t= 3.9449 sec.

e. Why would it be useful to be able to have equations for a roller coaster?

its safer and more efficient

f. What kinds of things might you be able to figure out about the roller coaster?

* is it fast?

* for how old of kids?

* is it possible for a ill people with heart and bleeding condition to ride it?

g. How might it help you to design or change the design?

it may become faster? or higher