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Active Calculus - Multivariable

Preview Activity 10.4.1.
As CEO and Head of Engineering at Steer Clear, you decide that you are almost ready to start testing your self-driving car out on the road. Your navigation and telemetry software will use the location tracking system (LTS) to determine all of the important information about how the car is moving and how adjustments need to be made. Before you start programming your software, you decide to drive on a quiet, country road and collect data from the LTS to use as test data for your programming. In other words, you will drive on a section of road you already have mapped out in order to check that your software is calculating the correct information. The map in Figure 10.4.2 below shows the path you plan to take on the country road (with the direction given by the arrows on the plot). Notice that at points \(B\) and \(F\text{,}\) the road crosses itself to go in a different direction.
The path of a car ride with seven points labeled
The path of a car ride with seven points labeled
Figure 10.4.2. The path taken on a country road to collect data with your LTS
(a)
At each of the labeled points on the curve, draw a vector in the direction of travel. Write a sentence about how you are determining this vector at the various points.
(b)
At each point, decide whether the car is turning left or right. Write a sentence about how you are determining this turning based on the plot given.