# 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?

##### 1 Answer

Apr 21, 2016

#### Answer:

This is a vector addition problem. The boat velocity vector and the river velocity vector need to be added to a resultant vector.

#### Explanation:

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