A boat that can move 50 km/h, wants to cross a 2 Km wide river, with current of 20 Km/h. Discuss what direction should the boat go to for the shortest distance to the bank. Discuss now what route will result in shortest time?
This is a vector addition problem. The boat velocity vector and the river velocity vector need to be added to a resultant vector.
The angle (a) of the two vectors is the direction upstream that must be taken to minimize the distance (2km) crossing directly across the river.
The shortest time will be a path perpendicular to the river, resulting in a transit time of 2km/50km/h = 0.04h (2.4min) and landing 20km/h * 0.04h = 0.8km downstream from the departure point on the opposite bank.
cos a = 50/53.85 = 0.928 a = 21.8 degrees