Kinematics in 2 Dimensions: Vector addition

In summary, the problem involves vector addition and using the theorem of Pythagoras to find the magnitude of A + B. The data and diagram are provided and the equations used are explained. The mistake in the solution is identified as using the wrong trigonometric functions for the angle of 141.9 degrees. The correct components for B vector are By = 8.3cos(51.9) and Bx = -8.3sin(51.9).
  • #1
huybinhs
230
0

Homework Statement



With the diagram and the data answer the question: What is the magnitude of A + B?

http://i995.photobucket.com/albums/af79/huybinhs/w.gif

DATA: theta1 = 33.7 deg, theta2 = 141.9 deg , A = 3.6cm, B =8.3cm.

Homework Equations



This is an example of vector addition. You have to add the x and y components independently and then use the theorem of Pythagoras. The figure is not to scale.

The Attempt at a Solution



I did as follow:

Ax = 3.6 * cos(33.7) = 2.995 m

Ay = 3.6 * sin(33.7) = 1.997 m

Bx = - 8.3 * sin (141.9) = -5.121 m

By = 8.3 * cos 141.9 = -6.532 m

A+B = sqrt[ (2.995 -5.121)^2 + (1.997 - 6.532)^2 ] = 5.001 = answer, but it's showing wrong!

Could u tell me what's wrong? Thanks!
 
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  • #2
Thats not good what i wrote. your mistake is with the By that shouldn't be negative. as it is positive
 
  • #3
Thaakisfox said:
Thats not good what i wrote. your mistake is with the By that shouldn't be negative. as it is positive

If so, 9.297 = answer => still INCORRECT :( ?
 
  • #4
You messed it up with sine and cosine of the 141.9 angle. Calculate the components of the B vector again.
 
  • #5
Thaakisfox said:
You messed it up with sine and cosine of the 141.9 angle. Calculate the components of the B vector again.

so, I agree By will be positive, but By = 8.3 * cos(141.9) which is negative number! I'm confused!
 
  • #6
Yes. take a look at the diagram. if you take cos(141.9) what you get is not By. since 141.9 is an angle greater than 90 degrees so actually you will get the negative of Bx.
To get the correct answer take By=8.3cos(141.9-90) and Bx=-8.3*sin(141.9-90).
 
  • #7
Thanks! Got it finally! ;)
 

1. What is kinematics in 2 dimensions?

Kinematics in 2 dimensions is the study of the motion of objects in two-dimensional space. It involves analyzing the position, velocity, and acceleration of an object as it moves in both the x and y directions.

2. What is vector addition in kinematics?

Vector addition in kinematics is the process of combining two or more vectors to find the overall displacement or velocity of an object. This is done by adding the individual components of each vector together to create a resultant vector.

3. How do you add vectors in 2 dimensions?

To add vectors in 2 dimensions, you must first break them down into their x and y components. Then, add the x components and the y components separately to find the resultant vector. The magnitude of the resultant vector can be found using the Pythagorean theorem.

4. What is the difference between displacement and velocity?

Displacement is a vector quantity that refers to the overall change in an object's position relative to its starting point. Velocity, on the other hand, is a vector quantity that describes the rate of change of an object's displacement over time. In other words, velocity is the object's displacement divided by the time it took to cover that displacement.

5. How is acceleration calculated in 2 dimensions?

In 2 dimensions, acceleration can be calculated using the equation a = ∆v/∆t, where ∆v is the change in velocity and ∆t is the change in time. This can be broken down into its x and y components to find the acceleration in each direction.

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