When Sam found out that teen pop sensation ... - Bob Hope School

Fan Club (pp. 1 of 2) KEY
When Sam found out that teen pop sensation Callie Colorado was
going to be the guest of honor in their town’s fall parade, he almost
freaked out! (He was Callie Colorado’s number one fan.) On the night of
the parade, Sam arrived early and staked out a spot on the street right
next to the parade route.
Sam first spotted Callie when she was 87 feet down the street, and her
car was moving at a speed of 6 feet per second. When she passed in
front of him, Sam was only 20 feet away from her. (He let out a big
scream!)
©2010, TESCCC 08/01/10
20 ft v
Sam
Precalculus
HS Mathematics
Unit: 01 Lesson: 01
distance down the street
1) When Callie Colorado was 87 feet down the street, her visual distance (v) from Sam was
actually about 89.27 feet. Explain why.
87 feet is the horizontal distance between Callie and Sam, not the direct distance.
To find the visual distance, you must use the Pythagorean Theorem.
87 2 + 20 2 = v 2 , which yields v � 89.27 feet.
2) Complete the table to describe the given distances with respect to the time in seconds since
Sam first spotted Callie Colorado. Sketch the graph of visual distance as a function of time.
Time
(sec)
Distance
down the
street (ft)
Visual distance
between (ft)
t d V
0 87 89.27
1 81 83.43
2 75 77.62
4 63 66.10
6 51 54.78
8 39 43.83
11 21 29
12 15 25
* 14.5 0 20
3) Write a linear function to relate time in seconds (t) and the distance (d) down the street.
Then use this function to determine when* Callie Colorado was directly across the street from
Sam.
d = 87 – 6t
0 = 87 – 6t
t = 87/6 = 14.5
C.C.

Fan Club (pp. 2 of 2) KEY
©2010, TESCCC 08/01/10
Precalculus
HS Mathematics
Unit: 01 Lesson: 01
4) What function rule can be used to find the visual distance (v) between Sam and Callie in terms
of t (time in seconds)?
v(t) =
2 2
(87 - 6x) + 20
5) Use this function rule to complete the following table for selected values of t.
Time
(sec)
Distance
down the
street (ft)
Visual distance
between (ft)
t d v
A -5 117 118.70
B 13 9 21.93
C 16 -9 21.93
D 34 -117 118.70
6) Do your answers for point A (above) make sense in the context of the problem situation?
What could these numbers represent?
Yes. This could mean that 5 seconds before Sam spotted Callie, her car was 117 feet down the
street, at a visual distance of 118.7 feet.
7) Do your answers for point D (above) make sense in the context of the problem situation?
What could these numbers represent?
Yes. This could mean that 34 seconds after Sam spotted Callie, her car was 117 feet down the
street in the other direction (to the left), at a visual distance of 118.7 feet.
8) What restrictions, if any, must be placed on the domain of this function?
None. The domain of the function includes all real numbers (or, (-�, �)).
9) Are there any restrictions on the domain and range of the problem situation?
Since the closest Sam gets to Callie is 20 ft, the range would only include values greater than
or equal to 20 (or, [20, �)). The domain, however, is only limited by the amount of time Sam
may have stood on the street before or after he spotted Callie in the parade (or, by the length of
time the parade lasted, or by the length of the street, etc.).