Catching a Train Bill’s train leaves at 8:06 am andaccelerates at the rate of 2 meters per second per second. Bill,who can run 5 meters per second, arrives at the train station5 seconds after the train has left and runs for the train.(a) Find parametric equations that model the motions ofthe train and Bill as a function of time.[Hint: The position s at time t of an object havingacceleration a is s = 1 / 2 at2.](b) Determine algebraically whether Bill will catch thetrain. If so, when?(c) Simulate the motion of the train and Bill bysimultaneously graphing the equations found in part (a).
Catching a Train Bill’s train leaves at 8:06 am andaccelerates at the rate of 2 meters per second per second. Bill,who can run 5 meters per second, arrives at the train station5 seconds after the train has left and runs for the train.(a) Find parametric equations that model the motions ofthe train and Bill as a function of time.[Hint: The position s at time t of an object havingacceleration a is s = 1 / 2 at2.](b) Determine algebraically whether Bill will catch thetrain. If so, when?(c) Simulate the motion of the train and Bill bysimultaneously graphing the equations found in part (a).
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.4: Plane Curves And Parametric Equations
Problem 68E
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Question
Catching a Train Bill’s train leaves at 8:06 am and
accelerates at the rate of 2 meters per second per second. Bill,
who can run 5 meters per second, arrives at the train station
5 seconds after the train has left and runs for the train.
(a) Find parametric equations that model the motions of
the train and Bill as a function of time.
[Hint: The position s at time t of an object having
acceleration a is s = 1 / 2 at2.]
(b) Determine algebraically whether Bill will catch the
train. If so, when?
(c) Simulate the motion of the train and Bill by
simultaneously graphing the equations found in part (a).
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