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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)?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 15AEXP
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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)?
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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