How Do You Calculate Resultant Displacement in Vector Problems?

[anglum]

i do not have a protractor with me and am very new to physics at the college level and have not gotten the book yet do to my student loans not bein processed and released at this time... PLEASE HELP

the question on my homework i am having trouble with is as follows


go 83.9 paces at 188 degrees

turn to 128 degrees and walk 199 paces

then travel 73 paces at 179 degreess

find the magnitude of the resultant displacement from the starting point, answer in units of paces.

and what is the direction of the resultant displacement? use counterclockwise from due east as the positive angular direction between the limits of-180 degrees and +180 degrees. answer in units of degrees.

 

[rocomath]

you need to show work b4 help is given, but here is a thought: in what direction do we go when we speak of degrees, counter-clock or clock-wise?

 

[anglum]

it does not say ... what i typed is word for word what the problem was... I am goin to assume counter clockwise from due east due to the last part of the last question

if you can help me i would be ecstatic

 

[anglum]

i don't even know how to begin this problem... this is my first physics course and i haven't been able to get the book yet due to my student loans not coming in... i tried to diagram it out but i don't have a protractor so i couldn't get the angles right for the diagram method with scaling...

and mathematically i am not sure of what procedure to even take

im sorry i am totally lost in physics... this is the only problem i cannot figure out

 

[rcgldr]

Think of this as a math problem, not a physics one. Forget the protractor, think about creating a graph.

 

[anglum]

i am tryin to make a graph but i can't figure out how to draw it correctly god i am such a moron right now... i figure i need to do this...

x component ...

a to b ... 83.9 x cos(188) = number and what direction?

b to c ... 199 x cos (128) = number and what direction?

c to d ... 73 x cos(179) = number and what direction?

i then add the numbers but the directions determine the +/- of the numbers

i then do the same for the y components but with the sin of the angles

and then i use those 2 final numbers to put into the pythagorean theorem?

i just am not sure what directions the numbers are in in each component for each a to b, b to c and c to d

and also am not sure becuz the cos of those angles = negative numbers

am i close?

please help me

 

[rcgldr]

am i close?

Yes, you have basically figured it out.

and also am not sure becuz the cos of those angles = negative numbers

You're corrrect, those are negative numbers.

 

[anglum]

but jeff if i use the cos of any of those angles it is a negative number? and how do i know what direction each is in?

can u help me with that

do i use cos for the x components and sin for the y components?

and what directions is a to b? b to c? c to d?

 

[anglum]

so all i really need is the directions to be correct then?

if the cos of them is all negative won't my final answers be negative? does that even matter?

 

[rcgldr]

and what directions is a to b? b to c? c to d?

That was stated in the problem, a to b is direction 188 degrees, b to c is direction 128 degrees ...

Try doing a simple example first:

100 paces from the starting point, direction -90 degrees, where are you now? Next 100 paces from this point, +90 degrees, where are you now?

Next example:

100 paces, direction 0 degrees, then 100 paces +90 degrees, then 100 paces +180 degrees, then 100 paces 270 degrees.

 

[rcgldr]

if the cos of them is all negative won't my final answer be negative? Does it matter?

No, it doesn't matter. It's ok to have negative movement.

 

[anglum]

so for my problem would the directions be as follows?

x component

a to b = west
b to c = east
c to d = west

y component

a to b = south
b to c = south
c to d = north

?

 

[rcgldr]

so for my problem would the directions be as follows?

x component

a to b = west
b to c = east
c to d = west

y component

a to b = south
b to c = south
c to d = north

Yes, you could combine a to b and call it south west.

 

[anglum]

so if all my directions are correct

i get for the x component

a to b = -83.9 west
b to c = -122.52 east
c to d = -72.989
x resultant = -34.36 west?

and for the y component

a to b = -11.68 south
b to c = 156.81 south
c to d = 1.27 north
and the y resultant is 143.860 south?

so then i square both and add them together? and then take the square root of that to get the first answer?

 

[anglum]

jeff do u know the final answer to this problem... so that when i get an answer u can tell me if I am right?

 

[anglum]

would b to c be north west? and c to d for that matter?

 

[anglum]

jeff u still here?

 

[learningphysics]

You don't need to worry about the directions for each part... just keep track of the numbers...

83.9*cos(188) = -83.08... I just noticed that you had a different number.

 

[anglum]

sodo i just add all those numbers up regardless of direction ? and just disregard the negative numbers and take them as positive numbers?

i have entered 5 diff answers to my online class all are wrong?

can u show me ur work if possible thanks

what are the resultants for the x components and what are they for the y components?

i have for the x components it is 279.409 and for the y components it is either 146.4 or 169.76?

if these are wrong can u correct them and show me how u got the correct ones please

please help... time is running out lol

 

[learningphysics]

When I add all the x-components I get: -278.589 paces

When I add the y - components I get: 146.4115 paces

The important thing to remember is that the signs take care of the direction... so don't worry about the direction till the end of the problem...

Did you get these same numbers?

 

[rcgldr]

I'm going to bed in just a bit. You've got the right idea, just add up all the X components, and Y components. If they're negative, then leave them negative, and add them up.

 

[anglum]

so learning... i then take the -278.589 and square that as well as the 146.4115 and then add them together... i take that answer and take the square root and that gives me the distance in paces from my starting point A to point D?

 

[learningphysics]

sodo i just add all those numbers up regardless of direction ? and just disregard the negative numbers and take them as positive numbers?

i have entered 5 diff answers to my online class all are wrong?

can u show me ur work if possible thanks

what are the resultants for the x components and what are they for the y components?
please help... time is running out lol

No keep the signs... the x-component is the (number of paces)*$$cos\theta$$. That's the answer! Whatever the sign is keep it... and don't worry about north/south/east/west... Same way the y-component is: (number of paces)*$$sin\theta$$

 

[learningphysics]

so learning... i then take the -278.589 and square that as well as the 146.4115 and then add them together... i take that answer and take the square root and that gives me the distance in paces from my starting point A to point D?

Yes, but check it yourself to make sure it's right. I might have made a mistake. So I get: 314.719 doing that...

 

[anglum]

so learning... i then take the -278.589 and square that as well as the 146.4115 and then add them together... i take that answer and take the square root and that gives me the distance in paces from my starting point A to point D? which gives me 314.719174?

 

[rcgldr]

so learning... i then take the -278.589 and square that as well as the 146.4115 and then add them together... i take that answer and take the square root and that gives me the distance in paces from my starting point A to point D?

Yes, assuming your numbers are correct.

 

[learningphysics]

so learning... i then take the -278.589 and square that as well as the 146.4115 and then add them together... i take that answer and take the square root and that gives me the distance in paces from my starting point A to point D? which gives me 314.719174?

Yes, but check the numbers.

 

[anglum]

that was correct and i had entered 315 as an answer earleir and it didnt take it... damn computer classesnow to get the angle it is 146.4115/-278.589 = Z
then i take the invtan of Z and that is my angle?

 

[anglum]

which gives me an angle of -27.724? but how do u have a negative angle?

 

[learningphysics]

that was correct and i had entered 315 as an answer earleir and it didnt take it... damn computer classes


now to get the angle it is 146.4115/-278.589 = Z
then i take the invtan of Z and that is my angle?

But be careful... there are 2 angles that have the same tan... now you know the total displacement is -278.589 in the x direction, and 146.4115 in the y-direction... so this angle is between 90 and 180 degrees.

 

[anglum]

so would i take 180 - 27.724?

 

[learningphysics]

which gives me an angle of -27.724? but how do u have a negative angle?

Remember that there are two angles with the same tan... the other angle is 180 + this angle.

 

[learningphysics]

so would i take 180 - 27.724?

yes, exactly.

 

[anglum]

so the angle for my answer is 152.276?

 

[anglum]

learning that was correct!1

thank you sooo sooo much

i appreciate your time, effort, and courtesy