How Do You Calculate the Displacement of a Car's Journey?

In summary: The angle would be 45 degrees, the angle, and the direction would be NE. Is that correct?In summary, the car's displacement is 16 km WNW and its average velocity is 11.3 km/3 hours NE. When determining the direction of a displacement vector, it is important to measure the angle it makes with the horizontal rather than relying on general directions such as NW or WNW. This can be done by measuring clockwise from vertically up, with N being 0 degrees and W being -90 degrees.
  • #1
Medgirl314
561
2

Homework Statement


A car travels 8 km E, then 8 km N, thrn 16 km W. What is the car's displacement?


Homework Equations



a^2+b^2=c^2

The Attempt at a Solution



R^2=8 ^2+8^2
R=11.3 km.

The resultant, R, seems to be 11.3, but I don't think this is the final answer, because I haven't take the 16 km into account yet. What's the next step?

Thanks in advance for a reply!
 
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  • #2
Grinding through the math is one thing, understanding it is another.

Have you tried making a sketch of the problem?
 
  • #3
If you follow SteamKing's advice, you'll find the problem to be totally trivial
 
  • #4
Thanks for your replies!

Agreed, I'm never satisified until I find the answer. I drew a diagram, and I'm attempting to find the answer using the parallelogram method. However, my visualization skills don't seem to be kicking in. I have a diagram that does look like a parallelogram, and it can be divided into two right triangles. Working from either side, it appears that the resultant is 11.3, but that doesn't seem complete.
 
  • #5
Medgirl314 said:
Thanks for your replies!

Agreed, I'm never satisified until I find the answer. I drew a diagram, and I'm attempting to find the answer using the parallelogram method. However, my visualization skills don't seem to be kicking in. I have a diagram that does look like a parallelogram, and it can be divided into two right triangles. Working from either side, it appears that the resultant is 11.3, but that doesn't seem complete.

Basically you have a right angled triangle with a and b both equaling 8 units

http://cdn.imghack.se/medium/200a3d66481a86f4584664ee2dbd0160.jpg

So your answer is correct as far as I can see
 
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  • #6
Great, thank you! I suppose the 16 came in indirectly. I thought it was odd because the answer is the same as one of my practice problems, so it just seemed too easy.
 
  • #7
So the distance traveled would be 32 km and if the trip took three hours, the average veocity would be 10.6 km/h NE, correct? And the speed would be 10.6 km/h?
 
  • #8
Medgirl314 said:
So the distance traveled would be 32 km and if the trip took three hours, the average veocity would be 10.6 km/h NE, correct? And the speed would be 10.6 km/h?
There's an interesting distinction between average speed and average velocity when the path is not a straight line. For average speed you take the total distance traveled along the path, but for average velocity you just look at the vector connecting start and end points - the path is irrelevant.
 
  • #9
Are you saying that my answer is correct, but the NE part isn't needed? My physics teacher noted that it was important, though that may go against the norm.
 
  • #10
Medgirl314 said:
Are you saying that my answer is correct, but the NE part isn't needed? My physics teacher noted that it was important, though that may go against the norm.

No, what haruspex was saying was that the answer for the average speed and the average velocity are not the same. For speed, you take the distance traveled divided by time, but for velocity, you use the displacement, a vector, which is the difference between the final and initial position vectors, and divide this by time.
 
  • #11
Thank you! Would the velocity be 11.3 km/3 hours?
 
  • #12
Yes, but since displacement is a vector, you need the direction as well.
 
  • #13
Right, so would that be ENE? Judging by the direction of my resultant?
 
  • #14
Medgirl314 said:
Right, so would that be ENE? Judging by the direction of my resultant?

The displacement vector is going north west. (Look at the img I attached above - the hypotenuse)

It may be better to use ° though, depends on preference.
 
  • #15
Medgirl314 said:
Right, so would that be ENE? Judging by the direction of my resultant?

Look at FaraDazed's drawing. On that page, straight up is north, straight left is west, etc. What direction is your resultant on the page. More importantly, what angle does it make with the horizontal?
 
  • #16
FaraDazed, we don't give complete solutions or give away answers on PF. Since you've done so, we have no idea if the OP understands how to determine the direction.
 
  • #17
Okay, I see it now. I looked at my drawing, which was flawed. It would be NW. Or maybe phrashing it like my teacher does, WNW.
 
  • #18
Medgirl314 said:
Okay, I see it now. I looked at my drawing, which was flawed. It would be NW. Or maybe phrashing it like my teacher does, WNW.

Actually, NW, and WNW are two totally different directions. A precise way to specify the direction is with an angle. Suppose we measure angles clockwise from vertically up (north). Then N means the vector points at 0°, and W means the vector points at -90°. What direction is NW? How about WNW? What direction is your vector pointing in?
 
  • #19
Oh, I didn't know that! Thank you. My teacher just said "Well, this resultant is pointing slightly more to the right than up, so it's ENE." Which made sense, it just wasn't explained. The degree explanation helps. Mine was pointing NW because my drawng was flawed.
 
  • #20
Medgirl314 said:
Oh, I didn't know that! Thank you. My teacher just said "Well, this resultant is pointing slightly more to the right than up, so it's ENE." Which made sense, it just wasn't explained. The degree explanation helps. Mine was pointing NW because my drawng was flawed.

Right, so can you tell me what angle your displacement vector points at, and what compass direction that corresponds to?

Northwest (NW) means "exactly between north and west". So, since N is 0 deg. and W is -90 deg, NW would be halfway between that, which would be -45 deg (or 360 - 45 = 315 deg, if you want to express angles as being between 0 and 360 only). This is NW.

West-northwest means "halfway between west and northwest". So, since west is -90 deg. and NW is -45 deg, halfway between that would be 22.5 degrees from each one. -45 - 22.5 deg = -67.5 deg.
OR, you could express the angle as 360 - 67.5 = 292.5. This is WNW.
 
  • #21
Oops, I meant mine was pointing northeast, not northwest. It would be exactly NE, 45 degrees, the way I drew it. But that was the wrong drawing.
 
  • #22
Medgirl314 said:
Oops, I meant mine was pointing northeast, not northwest. It would be exactly NE, 45 degrees, the way I drew it. But that was the wrong drawing.

When I say "your vector", I don't mean, "the one that you had in your incorrect drawing." I just mean, "the one in this problem that you are trying to solve."

The displacement points NW in this problem as you stated. But, to confirm that, you have to verify that it is at a 45 degree angle and not some other angle. I just wanted to make sure that you knew how to do that, which is why I insisted that you compute the angle, and not merely state, "it's NW."
 
  • #23
Oh! I thought we already confirmed that, so I wasn't sure what you were trying to show me. In that case, it would be a 45 degree angle, which I could verify with a protractor, but it makes more sense to just look at the compass rose. Thanks for the trick!
 
  • #24
Medgirl314 said:
Oh! I thought we already confirmed that, so I wasn't sure what you were trying to show me. In that case, it would be a 45 degree angle, which I could verify with a protractor
You really should verify it algebraically. What is the net displacement in the N direction? In the W direction? How do you deduce the angle from those two?
 
  • #25
It would be exactly between north and west, so -45 degrees. Is there a specific formula I'm suppossed to be using? The answer, degree-wise, seems a bit obvious to me because the angle is a 45 degree angle, and it is pointing in the negative direction. Thanks again!
 
  • #26
Medgirl314 said:
It would be exactly between north and west, so -45 degrees. Is there a specific formula I'm suppossed to be using? The answer, degree-wise, seems a bit obvious to me because the angle is a 45 degree angle, and it is pointing in the negative direction. Thanks again!
Measuring the angle in the standard navigational way, degrees clockwise from N, you would use tan(θ) = eastern displacement/northern displacement.
 
  • #27
Ah, okay. Thank you! My physics teacher hasn't gone into that yet, and so would perfer that I give the direction according to N/S and so on, but that's a great aid!
 
  • #28
cepheid said:
FaraDazed, we don't give complete solutions or give away answers on PF. Since you've done so, we have no idea if the OP understands how to determine the direction.

Sorry. I didn't think, I thought the "answer" would be it given in degrees.
 
  • #29
Medgirl314 said:
Ah, okay. Thank you! My physics teacher hasn't gone into that yet, and so would perfer that I give the direction according to N/S and so on, but that's a great aid!

Even so. You should know of have heard of degrees and what it represents in a circle? I.e east is 90°, south is 180° etc you should be able to work out what North West is.
 
  • #30
Sorry for the late reply!

I do, but I don't have the time at the moment to work out many extra problems at the moment, as I'm taking two other math courses as well as several other subjects, but I really appreciate the in depth explanation! I expect it will come in handy soon. :-)
 

Related to How Do You Calculate the Displacement of a Car's Journey?

What is displacement?

Displacement is a measure of the distance and direction of an object's change in position from its starting point to its ending point.

How do you calculate displacement?

To calculate displacement, you need to know the starting position and the ending position of the object. You then subtract the starting position from the ending position to get the displacement.

What units are used to measure displacement?

Displacement is typically measured in units of length, such as meters (m) or kilometers (km). It can also be measured in other units, such as feet (ft) or miles (mi), depending on the context.

What is the difference between displacement and distance?

Displacement is a vector quantity that takes into account the direction of an object's movement, while distance is a scalar quantity that only measures the total amount of ground covered by an object.

Can displacement be negative?

Yes, displacement can be negative if the object moves in the opposite direction of its starting position. This indicates that the object has moved backwards or in the opposite direction of its initial movement.

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