1. TERM 2013-2014 MATHEMATICAL PROJECT Name: Khlifa rashid hilal Class:12/04

2. ROLLER COASTER FUN

3. TASK 1: EQUATION MODELING 1. 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)=-0.5+40 a.How long does the ride last (from starting height to reaching ground level)? h(t) = 0 -0.5t+40 = 0 -0.5t = -40 T = 80 sec

4. b. change the numbers so that the ride starts higher and drops faster. h(t)=-5t+100 High velocity High height c. Now how long does the ride last, based on the changes in part b? h(t) = 0 -5t+100 = 0 -5t = -100 T = 20 sec

5. QUESTION 2: 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 2 -44t+96

6. a. What is the starting height of this ride?

7. b. How long is the rider below the ground? t=0 h(t) = 8t-44 h(0) = 8(0)-44 = -44m (bellow the ground) c. If the ride lasts a total of 10 seconds, what is the height of the exit gate? t=10 sec h(10) = 8(10)-44 = 36m

8. d. Use the information from the parts above to sketch a graph of the height of the ride over time with the appropriate labels on the axes. h(t)=8t-44

9. QUESTION 3: THE SCREAM This ride lasts for 8 seconds. The height of the rider can be modeled by the function: h(t)=(-6t 2 +12t)-(t 2 -12t+32)

10. a.At which height does this ride begin? t=0 h(t) = (-6t 2 +12t)-(t 2 -12t+32) h(0) = (-6(0) 2 +12(0)) - ((0) 2 -12(0)+32)-(0)t 4 = 0m b. At what height does this ride end? T=8 H(8) = (-6(8) 2 +12(8)) - ((8) 2 -12(8)+32) =0m

11. c. At what height is the ride after 5 seconds? T=5 h(t) = (-6t 2 +12t) - (t 2 -12t+32) h(0) = (-6(5) 2 +12(5)) - ((5) 2 -12(5)+32) = -90 m d. At what time(s) does the ride hit ground level? h(t)=0 / t=? 0 = (-6t 2 +12t)-(t 2 -12t+32) -6t 2 +12t = 0 or t 2 -12t+32 = 0 T=2 sec, t=0 sec t=8 sec, t=4 sec The ride hits the ground at t=0,2,4,8 seconds.

12. Sketch a graph of the ride with the appropriate labels on the axes. You may use you’re the Grapher program and experiment with the WINDOW to get the right picture.(copy paste your graph below)

13. f. Using the graph from part e, over what interval(s) of time does the ride drop below ground level. The ride drops below ground level over the interval [ 2,4 ]