Precalculus HS Mathematics Unit: 01 Lesson: 01

Bungee Jumper KEY Suppose that the function 3

2

h(t ) = 5t − 38t + 28t + 189 can be used to model the bungee jumper’s height in terms of time for 0 ≤ t ≤ 6. Complete the table to show the height (h in feet) of a bungee jumper at given values of time (t in seconds).

t (sec) 0 1 2 3 4 5 6

h (ft) 189 184 133 66 13 4 69

Questions: 1)

Describe a good graphing window for this function. Sample: Xmin = 0, Xmax = 6 (Xscl = 1) Ymin = 0, Ymax = 200 (Yscl = 10)

2)

How tall was the platform from which the daredevil jumped? How do you know? 189 feet. This is the value of h at t = 0.

3)

The bungee jumper went up a little into the air before she started to fall. How many feet above the platform did she jump? When did the peak of this jump occur? At t = 0.4 seconds, the jumper was 194.44 ft high. This means she jumped 194.44 – 189 = 5.44 feet above the platform.

4)

What is the closest that the bungee jumper came to the ground? After how many seconds into the jump did this point occur? At t = 4.67 seconds, the jumper was only 0.26 ft high from the ground.

5)

At t = 5 seconds, was the bungee jumper falling down or bouncing back up? Explain. Bouncing back up. At t = 5, the height is 4 feet (higher than the low point described in #4).

6)

Since h(t) passes through the point (4, 13), it is correct to say: “At t = 4 seconds, the jumper is falling.” However, it is incorrect to say: “At h = 13 feet, the jumper is falling.” Why? There are two times, at t = 4 and approximately at t = 5.27, at which the height of the jumper is 13 feet. One point occurs when the height is decreasing, and the other point occurs when it is increasing.

7)

©2012, TESCCC

Evaluate the function at t = 7. Does this value make sense in the context of the problem? Explain your reasoning. h(7) = 238 ft. This doesn’t make sense because the bungee jumper could not bounce back higher than the original platform. Also, as stated in the problem, the domain is restricted to values of t from 0 to 6, inclusive (0 ≤ t ≤ 6). 05/15/12

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