
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).

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:

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.

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.
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Precalculus
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