Finding the Velocity Vector Given Speed and Direction

We can be given a velocity in more than one way. One way is to be given a speed together with a bearing. The velocity can be found using trigonometry.

Example: A car is travelling at 50m/s on a bearing of 240 degrees. Find the velocity.

The vertical componenent of the velocity is

The horizontal component of the velocity is

The velocity is

We may be given the direction as a vector. If we are told the speed is 8m/s in directionwhich has magnitudethen we can compare the speed with the length of this vector. It istimes bigger, so we can multiplyby 1.6 to get the velocity vector. It is