Solving Vectors: Tips and Tricks for Effective Problem Solving

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In summary: You can find the moment of inertia, also known as inertial mass, by integrating the second derivative of the displacement vector with respect to time: where I can't do that. vectors are confusing and I'm not very good at them. Can someone else help me with this problem?If you are not confident in your ability to solve for vectors, it might be best to seek help from a more experienced individual.
  • #1
link107
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Homework Statement


A man walks 5 m at 37degrees north of east and then 10 m at 60degrees
west of north. What is the magnitude and direction of his net
displacement

The answer is around 9.3m at around 120 degrees angle on the +x axis

Homework Equations


none


The Attempt at a Solution


http://img825.imageshack.us/img825/2570/vectors2.png

I have no idea what to do after I plot out the vector and connect tip to head. Can someone explain to me how to solve for vectors effectively?

Thank you
 
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  • #2
One way to go after it is to draw right triangles and use them to find the end points in XY coordinates of what you have in the drawing. See if you can figure out what I'm talking about.
 
  • #3
Another way is to resolve the vectors along x and y axis

5m 37degrees north of east can be written as cos(37)*5 along x-axis and sin(37)*5 along y-axis

similarly do it for other vector..

now add components along x and y-axis seperately and get new measurements along x and y axis

now use x2+y2 = (magnitude of resultant)2
for magnitude

and arctan(y/x) for direction of resultant vector.(x and y are values of new measurements along x and y axis) (angle obtained is the angle from +ve x axis)
 
  • #4
Draco27 said:
now use x2+y2 = (magnitude of resultant)2
for magnitude

You really surprise me. You can't figure out how to obtain the distance between two points given their coordinates, yet you advise others precisely on how this is done.
 
  • #5
Did i make a mistake??
 
  • #6
Draco27 said:
Did i make a mistake??

No you did not. That's why I am surprised. Why can't you apply this same knowledge to your problem about the moment of inertia?
 
  • #7
Basically i got it

But pls help me with the double integration

i mean how is it done??
 

FAQ: Solving Vectors: Tips and Tricks for Effective Problem Solving

1. What are vectors and why are they important in science?

Vectors are mathematical quantities that have both magnitude and direction. In science, they are used to represent physical quantities such as force, velocity, and displacement. They are important because they allow us to accurately describe and analyze various phenomena in the natural world.

2. How do you add or subtract vectors?

To add or subtract vectors, you can use the head-to-tail method or the component method. In the head-to-tail method, you place the tail of one vector at the head of the other and draw a new vector from the tail of the first to the head of the second. In the component method, you break down the vectors into their x and y components and add or subtract them separately.

3. What is the difference between a scalar and a vector?

A scalar is a quantity that only has magnitude, while a vector has both magnitude and direction. For example, temperature is a scalar quantity because it only has a numerical value, but velocity is a vector quantity because it has both a speed and direction.

4. Can vectors be multiplied?

Yes, vectors can be multiplied in two ways: dot product and cross product. The dot product results in a scalar quantity, while the cross product results in a vector quantity. These operations are used in various applications, such as calculating work done by a force or torque on an object.

5. How do vectors relate to real-world phenomena?

Vectors are used to represent many real-world phenomena, including motion, forces, and electromagnetic fields. For example, velocity is a vector that describes an object's speed and direction of motion, and force is a vector that describes the magnitude and direction of a push or pull on an object.

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