What is the total displacement of a delivery truck given its route and time?

  • Thread starter JackandJones
  • Start date
  • Tags
    Grade 11
In summary, the delivery truck traveled a total distance of 34 km and had a displacement of 16.67 km at an angle of 49.79 degrees north of east. This was calculated by splitting the total distance into three triangles and using trigonometry to find the x and y components of each vector, and then using the Pythagorean theorem and trigonometry again to find the total displacement and direction.
  • #1
JackandJones
16
0
A delivery truck drives 14.0 km [E], 6.0 km [N], 12.0 km [ N 15° E], and then 2.0 km [N 65° E]. This takes him 42 minutes. Calculate the truck's distance and displacement.


When you draw this diagram you basically get two triangles. One large triangle and one smaller triangle. You need to find displacement. For the large triangle you can use pythagorean theorem, for the small triangle---that is where I am having problems.

I split 12 km (N 15 degrees E) into components: so I got 12 x sin (15) and 12 x cos (15) for the one small triangle

I split 2 km (N 65 degrees E) into components so I got 2 x sin (65), and 2 x cos (65)

So the total for x = 4.92 km and y = 12. 45 km...

Now what do I do?? I was thinking Cosline Law: but I don't know what to sub in for Cos.

Any help is appreciated!
 
Physics news on Phys.org
  • #2
Try splitting it into three triangles...one big one (the first one with the 14 and 6 km legs, and the next one with the 12 km hypotenuse, and the last one with the 2 km hyphyotenuse. Then add up the lengths to get the distance traveled, and and use pythagorus and trig on the giant triangle (the one formed with the hypotenuse running from the start point to the end point) to get the displacemnt magnitude and direction. Be sure to draw a sketch!
 
Last edited:
  • #3
Okay I tried doing that...but I am not sure it is correct. Could you show me some calculations of what you got? And/or show me a diagram?!

I appreciate the help!
 
  • #4
I didnt carefully check your trig, but you already have found the x and y components of each of the last 2 vectors, and you can find the x and y components of the first vector in the same manner..to get the total displacement, that's the square root of the sum of the squares of the x and y components, R = sqrt [(sum of x)^2 + (sum of y)^2]. See here:
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html
To get the distance traveled, add up the actual lengths of travel.
 
Last edited:
  • #5
I got 25 km N 65 degrees E...that can't be right, can u try and calculate the final answer?
 
  • #6
You found the sum of the x components of the last 2 vectors, which is 4.92. Now add it to the x component of the first triangle, which is 14, to get the total resultant displacement in the x direction, R_x.

You have also found the y components of the last 2 vectors, which is 12.45. Now add it to the y component of the first triangle, which is 6, to get the total resultant displacement in the y direction, R_y.

Now use pythagorus to find R, and trig to find theta.
 

What is Grade 11 Question Help?

Grade 11 Question Help is a service that provides assistance and support to students in Grade 11 who are struggling with their coursework and examinations. It offers resources, tips, and guidance to help students improve their understanding and performance in their academic subjects.

Who can benefit from Grade 11 Question Help?

Grade 11 Question Help is designed for students in Grade 11 who are seeking additional support in their studies. It can benefit students who are struggling with specific subjects, need help preparing for exams, or want to improve their overall academic performance.

What types of resources are available through Grade 11 Question Help?

Grade 11 Question Help offers a variety of resources, including study guides, practice questions, video tutorials, and personalized support from experienced educators. These resources are designed to help students better understand their subjects and improve their study skills.

Is Grade 11 Question Help only for students in certain subject areas?

No, Grade 11 Question Help is available for a wide range of subjects, including math, science, English, history, and more. The service aims to support students in all of their academic subjects and provides resources and assistance for a diverse range of topics.

How can I access Grade 11 Question Help?

Grade 11 Question Help can be accessed online through its website or through a mobile app. Students can sign up for an account and access resources and support whenever they need it. Some schools may also offer access to Grade 11 Question Help through their own learning platforms.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
5K
  • Introductory Physics Homework Help
Replies
6
Views
4K
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
4K
  • Introductory Physics Homework Help
Replies
7
Views
1K
Back
Top