Written Problem 3: An Acura and a BMW are driving around an empty planar parking lot, represented by the xy-plane. The trajectories of the cars are given parametrically by 33 15 A(t) =(5t +3, - 2t) (the Acura), B(t)=| 21+ 2,i + 2- (the BMW), where t represents time in minutes. a) Show that these cars crash into one another at a certain time. b) Compute the slopes of the tangent lines to the cars' trajectories at the time of the crash. Give your answers in fraction form. c) If you did part (b) correctly, you should notice something geometrically interesting about the tangent lines. What do you notice, and what does it tell you about how the cars crashed (ex: did they crash head-on)?
Written Problem 3: An Acura and a BMW are driving around an empty planar parking lot, represented by the xy-plane. The trajectories of the cars are given parametrically by 33 15 A(t) =(5t +3, - 2t) (the Acura), B(t)=| 21+ 2,i + 2- (the BMW), where t represents time in minutes. a) Show that these cars crash into one another at a certain time. b) Compute the slopes of the tangent lines to the cars' trajectories at the time of the crash. Give your answers in fraction form. c) If you did part (b) correctly, you should notice something geometrically interesting about the tangent lines. What do you notice, and what does it tell you about how the cars crashed (ex: did they crash head-on)?
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:Written Problem 3: An Acura and a BMW are driving around an empty planar
parking lot, represented by the xy-plane. The trajectories of the cars are given
parametrically by
A(t) =(5t +3, – 21) (the Acura), B(t)=| 21 +-
15
,t² + 2
2
33
-* (the BMW),
4
where t represents time in minutes.
a) Show that these cars crash into one another at a certain time.
b) Compute the slopes of the tangent lines to the cars' trajectories at the time of
the crash. Give your answers in fraction form.
c) If you did part (b) correctly, you should notice something geometrically
interesting about the tangent lines. What do you notice, and what does it tell
you about how the cars crashed (ex: did they crash head-on)?
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