Finding the velocities of these segments?

[chinnie15]

Homework Statement

The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a constant speed of 20 um/s. The figure shows the trajectory of an E. coli as it moves from point A to point E. Each segment of the motion can be identified by two letters, such as segment BC.

Homework Equations

Displacement of segment=√(segment_x²+segement_y²)
θ=tan^-1(segment_y/segment_x)
v=displacement/Δt

The Attempt at a Solution

Because I think my confusion can be cleared with just on portion of this problem, let's use vector AB. Here is the question I am trying to answer: Calculate the x- and y- components of its displacement and of its velocity.

I have AB_x=50μm, and AB_y=10μm
The displacement is 50.99μm, 11° NE

The problem is finding the velocity, I don't know how to do it in this instance? It doesn't give a time really, just the constant speed of 20μm/s. I can't help but to think that I'm missing something completely obvious, but I just can't figure out what to do?

Thank you for any help!

 

[tiny-tim]

hi chinnie15!

(have a mu: µ )

Calculate the x- and y- components of its displacement and of its velocity.
…
The problem is finding the velocity, I don't know how to do it in this instance? It doesn't give a time really, just the constant speed of 20μm/s. I can't help but to think that I'm missing something completely obvious …

yes, you know it's 20, so all you need (to find the components) is the direction

 

[chinnie15]

Hello

Ooooh, ok. I was completely missing that for some reason, lol. So, is this correct, then? It just seems like there should be more to it?

AB_x = 20µm/s*cos(11.3°)=19.6µm/s
AB_y= 20µm/s*sin(11.3°)=3.92µm/s

Thank you!

 

[tiny-tim]

let's see ……

3.92/19.6 = 1/5, so yes! ​

(note that you didn't need to find the angle, you can read the tan straight off the graph, and then find sin and cos using pythagoras! )

 

[chinnie15]

Thank you!

Sorry I'm not great at spotting the obvious. Math and physics is def. not my strongest point, and it doesn't 'click' very well. I just need to get through this physics and the next level, then I'll be done (hopefully, lol). Thank you again for your help!

 

[chinnie15]

Wait... I have another question. I'm confused how to find the information for vector BC, since it's a vertical line. I have that the BC_x component=0µm, and BC_y=10µm. This, however, leaves the direction undefined? I'm assuming this is incorrect, but aren't the components the amount the points have moved in total (displacement), and not their actual location of the grid? Or do I have this wrong?

 

[tiny-tim]

hi chinnie15!

… aren't the components the amount the points have moved in total (displacement), and not their actual location of the grid?

yes, (0,10) is the displacement

but the question asks for the velocity, and tells you that its magnitude is 20 …

and it's parallel to (0,10), so it's … ?