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 a t 2 ]. 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).
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 a t 2 ]. 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).
Solution Summary: The author analyzes the equations that model the motions of the train and Bill as a function of time.
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).
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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