Vector Application: Finding True Speed and Direction

by Dr. Carol JVF Burns (website creator)
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Here is a classic problem that uses vectors for its solution:

A plane travels through still air at a given speed, in a specified direction.
A wind (with known speed and direction) blows, pushing the plane off its intended course.

What is the resultant (true) speed and direction of the plane?

Speed indicates how fast something moves.
Speed is a scalar quantity—it is represented by a number (with unit).
Here are examples of speed:

Velocity is speed together with direction of movement.
Velocity is a vector quantity—it has both size (speed) and direction.
When solving problems involving velocity, all the tools for working with vectors are available!

Bearings are a way to specify direction, often used in navigation.
You may want to review bearings before studying the following problem.

A Typical ‘Find True Speed and Direction’ Problem, with Detailed Solution

A plane flies through wind that blows with a speed of 35 miles per hour in the direction N 43° W.
In still air: the plane has a speed of 550 miles per hour; the plane is headed in the direction N 60° E.


Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Vector Application: Forces Acting on an Object

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
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(MAX is 10; there are 10 different problem types.)
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