Cambridge O Level Additional Mathematics · Syllabus 4037 · Vectors in Two Dimensions
Resultant Velocity
What is Resultant Velocity?
The single velocity that has the same effect as two or more velocities acting together, obtained by adding those velocities as vectors, component by component. A boat driven east at four metres per second through water that is itself moving north at three metres per second has resultant velocity four comma three metres per second relative to the ground. The magnitude of the resultant is the resulting speed, found by Pythagoras on its components, and its direction must always be reported against a stated reference such as north of east or anticlockwise from the positive x-axis. The resultant is generally shorter than the sum of the separate speeds, and is zero when the contributing velocities cancel exactly.
This definition is part of the Vectors in Two Dimensions chapter in Cambridge O Level Additional Mathematics.
Questions students ask about Resultant Velocity
How do you report the direction of a resultant velocity correctly?
Never as a bare angle: a number such as \(36.9^\circ\) could be measured from north, from east, clockwise or anticlockwise, and each choice names a different direction. State the reference explicitly, for example "\(36.9^\circ\) north of east". Reading \(\tan^{-1}\) straight off a calculator is not enough either, since it only returns values between \(-90^\circ\) and \(90^\circ\) and cannot by itself name a direction in the second or third quadrant.