# Question #85b24

Sep 3, 2017

a) 5 meters

#### Explanation:

Straight ahead (OK, may 1' turn) would be 23 + 14 = 37. Not one of the options.

Straight back (180' 'turn') would be 23 - 14 = 9, also not an option, but as a minimum displacement it also eliminates 5 meters as an option.

Therefore, all of the others (10, 15, 20, 25) are possible, depending on the turn angle. ONLY a) 5 meters is NOT possible of the choices.

Sep 27, 2017

a.) $5 m e t e r s$ is the displacement that is not possible in this scenario.

#### Explanation:

Since none of the directions of motion are given, any answer except a.) is a possible outcome or the change in displacement.

The change in displacement would depend only on the angle at which the runner turns after running the first $23 m$.

For example if the runner turns ${180}^{0}$ at the end of $23 m$ and runs back $14 m$, his change in displacement will be $9 m$ in his original direction. So if he were to run the second leg at a slight angle off ${180}^{0}$, then $10 m$ is possible.

At the same time, $5 m$ is not possible because he did not run far enough back to be within $5 m$ of his starting point.

The rest of the choices are all possible because his longest possible distance is $23 m + 14 m = 37 m$ where he has turned ${360}^{0}$ at the turn. Any shorter distance is then in the range.

There is an example of negative displacement here:
https://socratic.org/questions/can-displacement-be-negative