Calculate the components of the vector

In summary, the components of the vector representing a velocity of 40m/s and an 55 degree angle are -23m/s horizontally and 33m/s vertically. The angle of 55 degrees should be used in the calculations, rather than 180-55, in order to find the components in the first quadrant. Trigonometry can be used on a right angled triangle with the given information to find the components.
  • #1
MoreZitiPlease
107
0

Homework Statement


Calculate the components of the vector representing a velocity of 40m/s and an 55 degree angle.


Homework Equations


none


The Attempt at a Solution


180-55=125
40(sin125)=33
40(cos125)=-23
(-23,33)m/sec

correct?
 
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  • #2
Why did you take 180-55?

you could have just used the 55 degree angle...but it is still correct...
 
  • #3
not really..

40cos125=-23
40cos55=23

two diffferent answers
 
  • #4
...you would get the same resultant...but the vectors are the same, just in opposite directions
 
  • #5
I suppose it depends on what orientation you use, but generally I would have thought that cos(55) would be what was being asked for.
 
  • #6
MoreZitiPlease said:
not really..

40cos125=-23
40cos55=23

two diffferent answers

The answers would be definitely coming different. As you are using two different vectors. Why are you doing 180 - 55.Its just 55. And doing so you will get its x and y components.
When you take 180 - 55 then you are taking a vector which is in the second quadrant which is different from the vector in the first quadrant.And we want to find the component of the vector which is in the first quadrant.
 
  • #7
so I should use 55? In my textbook it showed 180-55, that's why I used 125. But that example involved a car route or something.
 
  • #8
MoreZitiPlease said:
so I should use 55? In my textbook it showed 180-55, that's why I used 125. But that example involved a car route or something.

Yes, you should use 55.

This is a prime example of focusing too much on equations and trying to follow previous methods without actually thinking physically about what you are trying to do.

Draw a right angled triangle, with the bottom angle of 55 degrees, and the length of the hypotenuse as 40. Now, the x and y components are the horizontal and vertical sides of the triangle, respectively. You should be able to use trigonometry on this triangle in order to find the components.
 
  • #9
ok, thx
 

Related to Calculate the components of the vector

1) What is a vector?

A vector is a mathematical object that represents both magnitude (size) and direction. It is typically denoted by an arrow indicating the direction and length representing the magnitude.

2) What are the components of a vector?

The components of a vector are the perpendicular projections of the vector onto the x, y, and z axes in three-dimensional space. They represent the magnitude of the vector in each direction.

3) How do you calculate the components of a vector?

To calculate the components of a vector, you can use trigonometric functions and the Pythagorean theorem. The x-component is found by multiplying the magnitude of the vector by the cosine of the angle it makes with the x-axis. Similarly, the y-component is found by multiplying the magnitude by the sine of the angle. The z-component can be found using the Pythagorean theorem in three-dimensional space.

4) What is the difference between a vector and a scalar?

A vector has both magnitude and direction, while a scalar only has magnitude. Scalars can be thought of as quantities that can be measured by a single number, while vectors require multiple numbers or components to fully describe them.

5) How are vectors used in science?

Vectors are used in many areas of science, including physics, engineering, and biology. They are used to represent forces, velocities, and directions in motion, as well as other quantities such as electric and magnetic fields. Vectors are also used in data analysis and computer science, particularly in machine learning and data visualization.

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