Where do they meet? Kelly started at noon 1t = 02 riding a bike from Niwot to Berthoud, a distance of 20 km, with velocity 15 v12 02 (decreasing because of fatigue). Sandy started 1t + 122 at noon 1t 02 riding a bike in the opposite direction from Ber- thoud to Niwot with velocity u112 20 (also decreasing 1t + 122 because of fatigue). Assume distance is measured in kilometers and time is measured in hours. a. Make a graph of Kelly's distance from Niwot as a function of time. b. Make a graph of Sandy's distance from Berthoud as a function of time. c. When do they meet? How far has each person traveled when they meet? с. A d. More generally, if the riders' speeds are vi12 and 1t + 122 and the distance between the towns is D, B u12 1t + 122 what conditions on A, B, and D must be met to ensure that the riders will pass each other? e. Looking ahead: With the velocity functions given in part (d), make a conjecture about the maximum distance each person can ride (given unlimited time).
Where do they meet? Kelly started at noon 1t = 02 riding a bike from Niwot to Berthoud, a distance of 20 km, with velocity 15 v12 02 (decreasing because of fatigue). Sandy started 1t + 122 at noon 1t 02 riding a bike in the opposite direction from Ber- thoud to Niwot with velocity u112 20 (also decreasing 1t + 122 because of fatigue). Assume distance is measured in kilometers and time is measured in hours. a. Make a graph of Kelly's distance from Niwot as a function of time. b. Make a graph of Sandy's distance from Berthoud as a function of time. c. When do they meet? How far has each person traveled when they meet? с. A d. More generally, if the riders' speeds are vi12 and 1t + 122 and the distance between the towns is D, B u12 1t + 122 what conditions on A, B, and D must be met to ensure that the riders will pass each other? e. Looking ahead: With the velocity functions given in part (d), make a conjecture about the maximum distance each person can ride (given unlimited time).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Where do they meet? Kelly started at noon 1t = 02 riding a
bike from Niwot to Berthoud, a distance of 20 km, with velocity
15
v12
02 (decreasing because of fatigue). Sandy started
1t + 122
at noon 1t
02 riding a bike in the opposite direction from Ber-
thoud to Niwot with velocity u112
20
(also decreasing
1t + 122
because of fatigue). Assume distance is measured in kilometers
and time is measured in hours.
a. Make a graph of Kelly's distance from Niwot as a function of
time.
b. Make a graph of Sandy's distance from Berthoud as a function
of time.
c. When do they meet? How far has each person traveled when
they meet?
с.
A
d. More generally, if the riders' speeds are vi12
and
1t + 122
and the distance between the towns is D,
B
u12
1t + 122
what conditions on A, B, and D must be met to ensure that the
riders will pass each other?
e. Looking ahead: With the velocity functions given in part (d),
make a conjecture about the maximum distance each person
can ride (given unlimited time).
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