The bacterium E. coli is a single-cell organism that lives in the gut of healthy

Question

The bacterium E. coli is a single-cell organism that lives in the gut of healthy animals, including humans. When grown in a uniform medium in the laboratory, these bacteria swim along zigzag paths at a constant speed of 15?m/s . The following figure shows the trajectory of an E. coli as it moves from point A to point E

Part A)

What is the magnitude of the bacterium's average velocity for the entire trip?

Express your answer to two significant figures and include the appropriate units.

Part B)

What is the direction of the bacterium's average velocity for the entire trip?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

E is at the point (40, -20)
The displacement of E from the origin, by Pythagoras is sqrt(40^2 + 20^2) = 44.721 um.
Total distance trvelled = AB + BC + CD + DE. Using Pythagoras again
AB = sqrt(100 + 2500) = 50.9902 um
BC = 10 um
CD = sqrt(100 + 1600) = 41.231 um
DE = sqrt(2500 + 2500) = 70.7107 um
Total = 172.932 um
Total time taken = distance/velocity = 172.932/15 =11.5288 s

1) Average velocity = displacement/time = 44.721/11.5288 = 3.879 um/s
2) Direction
sin theta = 20/40 = 0.5, theta = 30 degrees south of east

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