Motion in 2 dimensions -- Total displacememt of an ant walking

[danielsmith123123]

Homework Statement

An ant travels 2.78 cm [W] and then turns and travels 6.25 cm [S 40° E]. What is the ant’s total
displacement? Answer: [ans: 4.94 cm [E 76° S]]

Relevant Equations

Dt^2 = Dtx^2 + Dty^2

I got the answer right and here's my work, but I want to know how to get the final direction correct [E 76 S]:
Dtx = 2.78 [W] + (6.25)(sin40)
Dtx= 1.237

Dty= (6.25)(cos40)
Dty= 4.95

Dt= 4.95 (pythagorean thereom involving 1.237 and 4.95)

Dangle = tan^ (4.95/1.237) = 76

Therefore, it is displaced 4.95cm [E 76 S]

 

[hutchphd]

For your own benefit, draw a rough picture of the two vectors and consider your result. What do you think?

 

[kuruman]

Your calculations are all wrong.
For Dtx: 2.78 + (6.25)(sin40) = 6.797 not 1.237
For Dty: (6.25)(cos40) = 4.787 not 4.95

The known answer of 76^o does not follow from your work. It looks like you reverse-engineered the question using the known answer for the angle which not an approved way to solve physics problems. As @hutchphd already suggested, draw a picture and resolve the vectors into components. Then you will see what is going on.

 

[danielsmith123123]

Your calculations are all wrong.
For Dtx: 2.78 + (6.25)(sin40) = 6.797 not 1.237
For Dty: (6.25)(cos40) = 4.787 not 4.95

The known answer of 76^o does not follow from your work. It looks like you reverse-engineered the question using the known answer for the angle which not an approved way to solve physics problems. As @hutchphd already suggested, draw a picture and resolve the vectors into components. Then you will see what is going on.

I didn't reverse it, I simply copied both down wrong I'll show you my work

 

[kuruman]

The work that you show shows the same incorrect calculations that you posted. You show that
2.78 + (6.25)(sin40) = 1.237.
That is incorrect. You cannot add two positive numbers both of which are greater than 2 and get a number that is less than 2.
(6.25)(cos40) = 4.95 is also incorrect but not by much. Redo the calculations and see for yourself.

 

[jbriggs444]

The work that you show shows the same incorrect calculations that you posted. You show that
2.78 + (6.25)(sin40) = 1.237.

However, if you take 6.25 sin(40) - 2.78 then you do get 1.237.

Obviously, your point stands. We should not be forced to guess at a formula based on the calculated answer.

 

[kuruman]

However, if you take 6.25 sin(40) - 2.78 then you do get 1.237.

Obviously, your point stands. We should not be forced to guess at a formula based on the calculated answer.

Not only that, but the relative negative sign would be obvious if a diagram were drawn as suggested by @hutchphd.

 

[danielsmith123123]

Sir, if you looked at the picture I sent you:
- You would've saw my vectors; I added two opposite vectors meaning I changed the 2.78W into -2.78E . I did that to simply save space and time.
- I also did (6.25)(cos40) = 4.788 and I am not sure if you're telling me not to round from 4.787777769?
- The only "mistake" I made was change my final angle of 75.14* into 76* because that's what my textbook said.
Thank you for your time

 

[kuruman]

Sir, if you looked at the picture I sent you:
- You would've saw my vectors; I added two opposite vectors meaning I changed the 2.78W into -2.78E . I did that to simply save space and time.
- I also did (6.25)(cos40) = 4.788 and I am not sure if you're telling me not to round from 4.787777769?
- The only "mistake" I made was change my final angle of 75.14* into 76* because that's what my textbook said.
Thank you for your time

Thank you for clarifying that [W] translates to a negative sign. Had you written [E] next to 6.25 sin(40), I would have understood that you are using unit vectors. Your diagram in the picture you posted is useless. Besides being sideways, which makes it hard to read, the labels are illegible. Next time you post a picture, please show more consideration to those who view it.

 

[jbriggs444]

I also did (6.25)(cos40) = 4.788 and I am not sure if you're telling me not to round from 4.787777769

4.787777769 does not round to 4.95.

If one were rounding to multiples of 5 in the second decimal place, the correct rounding would be to 4.80.

 

[Steve4Physics]

Hi @danielsmith123123. If you are still reading this, note that @hutchphd and @kuruman are giving you excellent advice about drawing a diagram.

When I was at school (ahem years ago) my physics teacher used to go on and on about drawing a diagram as the very first step in answering most problems (even when it wasn't obvious that a diagram was relevant!). And if you forgot, he would remind you!

Drawing a good diagram helps you formulate the problem in your own mind, forces you to read the question carefully (to enable you to draw the diagram correctly) and often helps you to see how to solve the problem.

If it helps, here is the sort of diagram I'd draw here, to add the 2 displacements. I've shown the resultant in red.