You're going for a bike ride and start 7km north of the town and riding on a straight path that leads to a park 3km west of town. It takes 20 minutes to cover this distance. Write parametric equations expressing your motion, with the town being represented by the origin, and t=0 representing your starting point then find your location after 5 minutes using these parametric equations. Then eliminate the parameter to get a rectangular equation for this path and verify algabraically that this equation represents this line and that both the parametric and rectangular equations are the same. Suppose you ride back along the same path, but now t=0 represents the new starting point, which was the original ending point. Explain what changed in the parametrization and if the rectangular equation changed.
You're going for a bike ride and start 7km north of the town and riding on a straight path that leads to a park 3km west of town. It takes 20 minutes to cover this distance.
Write parametric equations expressing your motion, with the town being represented by the origin, and t=0 representing your starting point then find your location after 5 minutes using these parametric equations.
Then eliminate the parameter to get a rectangular equation for this path and verify algabraically that this equation represents this line and that both the parametric and rectangular equations are the same.
Suppose you ride back along the same path, but now t=0 represents the new starting point, which was the original ending point. Explain what changed in the parametrization and if the rectangular equation changed.
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