8.7 Computational Thinking
Example 1 - boat navigation
Let the coordinates be in km. A boat is at point (-40, -20) and is headed toward the point (50, 80) with a speed of 10 km/h. Compute the point where the boat needs to make a \(60^\circ\) turn to continue in a straight line towards the harbor at the point (40, 50). How long will it take the boat to reach the harbor?
Example 2 - boat navigation with a current
Lets revisit example 1, but now assume that there is a current flowing in the positive x-direction at 5 km/h. Compute the point where the boat needs to make a \(60^\circ\) turn to continue in a straight line towards the harbor at the point (40, 50). How long will it take the boat to reach the harbor?
Example 3 - boat navigation with a bad navigation system
In this situation the boat is unaware of the current flowing in the positive x-direction at 5 km/h. The boat is at point (-40, -20) and is headed toward the point (50, 80) with a speed of 10 km/h. Assume the boat takes the \(60^\circ\) turn at the same coordinates as in example 1. After turning the captain realizes that the boat is drifting off course. Every kilometer they correct their coarse by steering towards the harbor at (40, 50). How long will it take the boat to reach the harbor now? Plot the trajectory of the boat.