Why Is My Calculation for the X Component of the Vector Sum Incorrect?

[STEF2098]

The two vectors a and b have equal magnitudes of 13.0 m and their angles are θ1 = 30° and θ2 = 100°.
Find the components of their vector sum, r.


I know this is a very simple problem, but I can't get it! And it is frustrating me to no end.

I know the y component of the sum is 16.3. (I don't remember how I got this, but it's right.)
However, when I try to find the x components of each vector, I get 11.26 for a, and -2.26 for b. When these are added, you get 9.0. And the computer(our HW is graded online) is telling me that this is the wrong answer.

What am I doing wrong?!

 

[tiny-tim]

The two vectors a and b have equal magnitudes of 13.0 m and their angles are θ1 = 30° and θ2 = 100°.
Find the components of their vector sum, r.
…
I know the y component of the sum is 16.3. (I don't remember how I got this, but it's right.)
However, when I try to find the x components of each vector, I get 11.26 for a, and -2.26 for b. When these are added, you get 9.0. And the computer(our HW is graded online) is telling me that this is the wrong answer.

What am I doing wrong?!

Hi STEF2098!

hmm … I make it 9.0 also, but I don't get 16.3

are you sure it's not |a| = |b| = 11.0 m?

 

[kerimek]

It seems like you are on the right track with finding the y component of the sum, but there may be an error in your calculation for the x component. Let's break down the problem and see if we can find the mistake.

First, we can draw a diagram to visualize the problem. We have two vectors, a and b, with equal magnitudes of 13.0 m and angles of 30° and 100°, respectively.

Next, we can use trigonometry to find the x and y components of each vector. For vector a, the x component would be 13.0 m * cos(30°) = 11.26 m and the y component would be 13.0 m * sin(30°) = 6.5 m. Similarly, for vector b, the x component would be 13.0 m * cos(100°) = -2.26 m and the y component would be 13.0 m * sin(100°) = 12.3 m.

Now, to find the vector sum, we can add the x components and the y components separately. The x component of the sum would be 11.26 m + (-2.26 m) = 9.0 m. The y component of the sum would be 6.5 m + 12.3 m = 18.8 m.

Finally, we can use the Pythagorean theorem to find the magnitude of the vector sum, r. It would be √(9.0 m^2 + 18.8 m^2) = 21.1 m. And to find the angle of the vector sum, we can use the inverse tangent function: tan^-1(18.8 m/9.0 m) = 65.7°.

So, the final answer for the vector sum, r, would be 21.1 m at an angle of 65.7°. I hope this helps you identify any mistakes in your calculation and understand the problem better. Remember to always double-check your work and use diagrams to visualize the problem. Best of luck!