Problem 4-4
First Look
Comments
Before we generalize anything, above you can play around with the variables. The camper and tent can be moved, as well as point C on the river to change the path of the camper. Also, point A and B changes the location of the river. After placing the river, camper, and tent where I want, I move point C around to see when the distance is the lowest. It is 15.29 above based on where everything is placed.
Final Thoughts
Final Thoughts
If we reflect the tent over the river and make a line from the camper and the reflected tent (this line will intersect the river), we can make a segment from the camper to where this new line intercepts the river (at point D). This is our most optimal path to the river. Then we need to make a segment to represent going from this point on the river to the tent. This path is labeled our optimal path. The angles alpha and beta that come out of point D will always be the same, and this is why it is the shortest path.
I have kept point C so we can move it along the river. No matter what slope the river is at or where the camper and tent are (as long as they are on the same side of the river), then we can move C around to see that the shortest path is always where point D is.