The Vector Triathlon The map shown below gives several paths that can be taken from the start at the northern most location of Peterborg (Picara Point) to the finish at the Coast Guard dock in Charlotte Amalie. The options are color coded and are as follows: Swim at 1.0 m/s Run at 3.0 m/'s (actually yellow in the diagram) Bike at 6.0 m/s The grid size is 0.28 by 0.28 km. You have three tasks: 1. Find the fastest route from Start to Finish. You will need to find the time for each segment and then determine which combination of segments represents the least time. Assume all the speeds are averages that take into account the terrain. 2. Draw the total displacement vector. Write your chosen triathlon vector segments and the total displacement vector in components form (x, y). Show that the total displacement vector is indeed the sum of the chosen triathlon vector components. 3. Assume that there are no roads or paths, and that you must navigate the segments you have chosen by using a compass and an odometer. The compass will give you the direction (N, E, S, and W) and the odometer tells you how far you have traveled. So you must convert the description of each vector segment into the appropriate quantities that you will be able to use with the compass and odometer. | START Swim - 1.0 m/'s Bike - 6.0 1/S Run 30 TV5 Each grid mark is 0.28 km NIGHED Drake's FINISH Veteran Yacht Haven Grinds West Indian mer Company DockSTART Swim - 1.0 m/'s Bike - 6.0 71/5 Run 3.0175 Each grid mark is 0.28 km ENIGHED MISDEN FINISH ferans Yacht Haven Greed West Indian weymouth Rh mer twy Company Dock