displacement question..?

Question

if Doug leaves home on a trip to the lake that takes him to a position of 80km [W] of home, what is his displacement? do you know the distance that he traveled?

*ok. i really don't understand this question. can you explain the steps you took to solve this or any other displacement question?/
thanks!

Answer 1

The question is trying to discern the difference between vectors (displacement) and scalars (distance). Let's look at this.

Suppose you walk completely around a circle of circumference C = 1 mile, five times. You start at the 12 o'clock position and end there because you walked "completely" around the circle each time.

How far did you walk? You walked 5 miles because each trip around was 1 mile. That's the distance traveled. If you walked at |v| = 5 mph, it would take you t = D/|v| = 5C/5 = 5*1/5 = 1 hour to walk that five miles. |v| is the speed you walked; it is a scalar without direction. D is the distance you walked, it is also a scalar without direction.

Now, the fun part...your displacement is c1 - c0 = 0; where c1 is where you ended up on the circle and c0 is where you started from. In this example, both are at the 12 o'clock position; so c1 = c0 and, ta da, c1 - c0 = 0. And here you thought you walked five miles. Well, you did, but it literally got you nowhere because you ended up in the same place you started from. And that's the difference, for distance you don't care which direction you walked; for displacement you do.

Here's an even funner(?) thing about this. What do you suppose the average velocity (based on displacement velocity is also a vector) might be? Velocity is defined as v = delc/delt; where delc = c1 - c0 from above and delt = t1 - t0, the time of starting the walk t0 and ending it t1. Then v = (c1 - c0)/(t1 - t0) = 0/1 hr = 0 miles per hour. Aargh, all that walking and we averaged zero miles per hour velocity. Why? Because displacement was zero after all that time.

On the circle we could have traveled 1 time (1 mile) distance around that circle or a million times (1 million miles) distance around it; still the displacement would have been zero...nada, zilch, niente, nichevo, nichts.

So, just like the circle example, we have no clue the distance Doug traveled. Doug could have flown to Beijing China and back home, then driven to that position 80 km from his house. Or he could have driven straight from home. The displacement would have been the same in both instances, but the distances are obviously way different.

Answer 2

his displacement is 80Km West of where he started.
displacement is the straight line distance and direction an object is from a given place.
I don't know the distance he traveled, because he could have gotten there by a direct route or a round-about route