Explain Independence of Vectors Quantities

Perpendicular vector quantities are independent of one another.  This means that the actions of one vector will not affect the actions of another vector. The actions of both vectors determine the resultant. 

Let's consider the typical problem for independence of vector quantities:  the dreaded boat crossing the river problem. 

A rowboat is trying to cross the river to get to the picnic on the other side. The river current moves due southward at a rate of 3.0 m/s.  The person in the boat paddles due east at a speed of 4.3 m/s.

Because the boat vector and the current vector are perpendicular to each other, they do not affect each other in any way.  The boat's speed is independent of the current.  Similarly, the current is independent off the boat's speed.

Example 1:

If the river is 265 m wide, how long will it take for the boat to cross the river? 

Here s  where the independence of vector quantities comes in handy.  The speed of the boat across the river is unaffected by the current downstream.  The boat will continue to move due east at a speed of 4.3 m/s no matter what the current is. 

For now, the river current part of the problem was only added to throw you off the track.

To calculate the time it takes to cross the river on the boat, use the factor label method:

265 m * (1 s/ 4.3 m) = 61.6 s

Because the vector quantities are independent, we only needed to use the one in the right direction.