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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 of an object having acceleration is ].
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).
![Check Mark](/static/check-mark.png)
To find:
a. Parametric equations that model the motions of the train and Bill as a function of time. [Hint: The position s at time of an object having acceleration as is ].
Answer to Problem 51AYU
a. Train: , Bill’s: .
Explanation of Solution
Given:
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.
Formula used:
Calculation:
Let be train’s path; be bill’s path.
a. Train:
Bill:
![Check Mark](/static/check-mark.png)
To find:
b. Algebraically whether Bill will catch the train. If so, when?
Answer to Problem 51AYU
b. No, He cannot catch the train.
Explanation of Solution
Given:
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.
Formula used:
Calculation:
Let be train’s path; be bill’s path.
b.Bill will catch the train only when
does not have any real function as
Hence Bill cannot catch the train.
![Check Mark](/static/check-mark.png)
To find:
c. Simulate the motion of the train and Bill by simultaneously graphing the equations found in part (a).
Answer to Problem 51AYU
c.
Explanation of Solution
Given:
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.
Formula used:
Calculation:
Let be train’s path; be bill’s path.
c.
Chapter 10 Solutions
Precalculus
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
University Calculus: Early Transcendentals (4th Edition)
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