Comparing Distance and Displacement in a Two-Child Race

[Nachore]

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back Joan is ahead of Mike. Which statement is correct about the distances run and the displacements from the origin?
a. Joan has run a greater distance and her displacement is greater than Mike's.
b. Mike has run a greater distance and his displacement is greater than Joan's.
c. Joan has run a greater distance, but her displacement is less than Mike's.
d. Mike has run a greater distance, but his displacement is less than Joan's.
e. Mike has run a shorter distance, and his displacement is less than Joan's.


I really don't get this question. Aren't Joan and Mike running the same distance and displacement, because they are starting at the same place and ending at the same place?

 

[alphysicist]

Hi Nachore,

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back Joan is ahead of Mike. Which statement is correct about the distances run and the displacements from the origin?
a. Joan has run a greater distance and her displacement is greater than Mike's.
b. Mike has run a greater distance and his displacement is greater than Joan's.
c. Joan has run a greater distance, but her displacement is less than Mike's.
d. Mike has run a greater distance, but his displacement is less than Joan's.
e. Mike has run a shorter distance, and his displacement is less than Joan's.


I really don't get this question. Aren't Joan and Mike running the same distance and displacement, because they are starting at the same place and ending at the same place?

I think they mean for you to answer this question after they are both on the way back, but before they have reached the origin. What do you get?

 

[jdlinke]

alphysicist's suggestion makes sense. If we consider the time interval to be from t=0 to the point in the word problem where Joan is ahead of Mike (and we stop our time interval there. We're not considering anything further. Our analysis is just from the time they start, until the time described in the problem. They have not yet made it back to the origin), the problem makes sense. In this situation, the are starting at the same point, but end at differing points. At the end of the time interval we're looking at, Joan is nearer to the origin than Mike, and so the problem can be solved.

Hope that helps :)