Independence of Perpendicular Vectors Fact: Vector quantities acting on the same object, but in perpendicular directions, do not affect each other. Think back to the Paper River Lab… Did the river’s current make the boat’s motor go at a different speed? Did the boat’s motor make the river’s current go at a different speed? Note, these are not the same questions as: Did the river’s current make the boat follow a different path than the motor would have alone?

Some think the current will add time to crossing the river, since the boat obviously travels a longer distance… Others think the current will lessen the time to cross the river, since the current makes the boat move faster than with the motor alone… In a sense, both of these ideas have merit, but acting together, basically cancel out each other’s effects… watch...

Having the current there does affect the boat’s path… The current clearly acts on the boat in the downstream direction, forcing the boat to end up DS from where it started. And the current does affect the boat’s resultant speed… Not the speed the motor moves it, but the resultant speed from combining motor & current… So the extra distance the boat is moved because there is a current, is made up for by the current also adding proportionally extra speed to the boat to carry it that extra distance.

If the width of the river doesn’t change, and the boat’s motor speed doesn’t change, then the time it takes the boat to cross the river shouldn’t change, (as long as you point your boat directly across the river). Because by pointing your boat directly across the river, all of the boat’s velocity – the entire vector of it – is being used to get the boat across the river – which is exactly the same situation as if there had been no current at all. This is the idea of Independence of Perpendicular Vectors: If the current is acting perpendicular to the boat’s motor, it won’t affect what the motor is trying to accomplish for the boat at all – no help, no hurt. So a boat will take the same amt of time to cross still water, as a river of equal distance!

How Could You Have Seen This in the Paper River Lab? Now consider Proc 6, where you determined the % difference between the average times across the pond vs the average times across the river. How did that work out??? For the vast majority of lab groups, they turn out to be quite small… always under 10%... So by science standards, these values are considered to be within an acceptable margin of error, … and therefore, within reason, the same!! So you should have concluded that … the current of the river did not affect the time your boat took to cross it, as long as the boat was perpendicular to the flow of the current.