Headwinds or tail winds will change the course of the objects motion by changing its resultant velocity
A side wind will change its course by pushing it to the left or the right, causing the distance traveled to change
The Pythagorean theorem can be used to calculate the final distance
Riverboat problems are similar
Motorboat problems such as these are typically accompanied by three separate questions:
What is the resultant velocity (both magnitude and direction) of the boat?
If the width of the river is X meters wide, then how much time does it take the boat to travel shore to shore?
What distance downstream does the boat reach the opposite shore?
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Any vector - whether it is a force vector, displacement vector, velocity vector, etc. - directed at an angle can be thought of as being composed of two perpendicular components. These two components can be represented as legs of a right triangle formed by projecting the vector onto the x- and y-axis.
The resulting motion of a plane flying in the presence of a crosswind is the combination (or sum) of two simultaneous velocity vectors that are perpendicular to each other.
All vectors can be thought of as having perpendicular components.