The chart indicates the time, speed, and velocity of five runners.

which best describes the runners?

a. garreth and elisa ran the same distance but not the same displacement, luigi and jasmine went the same displacement, and logan ran faster than jasmine.
b. garreth ran farther than luigi, elisa and jasmine went the same distance, and logan and jasmine has the same displacement in the opposite direction.
c. garreth and elisa ran together, luigi and jasmine went the same distance, and logan and jasmine have the same displacement in the opposite direction.
d. garreth ran less than logan, elisa and jasmine went the same displacement, and luigi and garreth ran together.

The correct answer is:

c. Garreth and Elisa ran together, Luigi and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction.

Explanation:

First of all, let's remind the difference between distance and displacement:

- distance: this is just the distance covered by the person in any direction, and it is given by

- displacement: this is the distance between the final point and the initial point of motion, and it is given by

Now, Looking at the table, we can say that:

- Garreth and Elisa ran together: in fact, they had same speed, same velocity and same total time. This means that they cover same distance and same displacement - also in the same directio (west), so they ran together

- Luigi and Jasmine went the same distance: in fact, they ran with same speed in the same time, so their distance (which is the product between speed and time) is the same

- Logan and Jasmine had same displacement in the opposite direction: in fact, they ran with same velocity in the  same time, so their displacement (which is the product between velocity and time) is the same, just the direction is opposite (Logan ran north, Jasmine ran south)

6 cos 34, 6 sin 34 trig