you are able to swim at 1.4 m/s. one day you swim directly across a river that has a uniform water flow of 6.1 m/s. what is your resultant swimming velocity - both magnitude and direction (given as an angle with respect to the shore)?
Let V be the vector of my velocity, and U be the vector of water flow velocity. By assumption V and U are orthogonal, |V|=1.4, and |U|=6.1
If we choose plane coordinates (x,y) in which I have coordinate (0,0), V=(0, 1.4) directed up, and U=(6.1, 0) directed right, then the resulting vector is V+U = (6.1, 1.4)