Ferrix

Meet Ferrix, a little rowing boat who has learned to aim upstream to cross a river in a straight line.

A boat on a river has two velocities at once: its own velocity through the water, and the velocity of the water over the ground. What someone on the bank sees is the vector sum of the two.

Suppose Ferrix rows at 2.5 m/s through the water and the river flows at 1.5 m/s. To land directly opposite, he must point upstream so the sideways part of his rowing cancels the current. That needs an angle with sin θ = 1.5/2.5, about 37° upstream. His speed straight across is then √(2.5² − 1.5²) = 2.0 m/s.

If he points straight across instead, he crosses faster but lands downstream. If the current is faster than his rowing, he cannot reach the point directly opposite at all.

Pilots use exactly the same trick in a crosswind, pointing the nose of the aircraft partly into the wind so that the plane tracks straight along the runway.