BR Physics Confusion

[brisingr]

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This is in the translational motion chapter and it has been driving me nuts!

On page 14 it says that when the angle is less than 45 degrees Rx is greater than Ry. This makes sense to me since Rx= Rcostheta and Ry=Rsintheta.

In the question on the next page, however, Rx is 2400m and Ry is 3200m and it says that because the Rx component is smaller than the Ry component the angle must be less than 45 degrees.

Am I missing something here or is the second question a typo??

 

[shoehornlettuce]

Because the person is walking North and then West you don't have to separate into components. The 3200m will be your Y coordinate and 2400m will be your X coordinate. All you need to do to solve for distance is sqrt((2400^2)+(3200^2)). This gives you the magnitude which is 4000m.

Now draw out a triangle with hypotenuse 4000 and either X or Y coordinate will do. So lets use hypotenuse 4000 and the X coordinate (2400m). To find the angle you have cos(angle)=2400/4000 so the angle will be 53.1 degrees North of West or (90-53.1 = 36.9 degrees) West of North.

Make sure you pay attention to the answer choices. Because the answers are given as "West of North" the angle will be less than 45 degrees. If they said "North of West" it would be greater than.

 

[MedPR]

This is in the translational motion chapter and it has been driving me nuts!

On page 14 it says that when the angle is less than 45 degrees Rx is greater than Ry. This makes sense to me since Rx= Rcostheta and Ry=Rsintheta.

In the question on the next page, however, Rx is 2400m and Ry is 3200m and it says that because the Rx component is smaller than the Ry component the angle must be less than 45 degrees.

Am I missing something here or is the second question a typo??

It's not a typo.

cos30 = .86
cos45= .71
cos60=.5

sin30 = .5
sin45 = .71
sin60=.86

For Rx to be smaller than Ry, the angle must be less than 45 degrees. If you don't understand why, do some quick math. As you said, Rx=Rcostheta and Ry=Rsintheta.

If theta is 60 (bigger than 45) Rx < Ry
If theta is 30 (smaller than 45) Rx > Ry

 

[brisingr]

Thanks a lot guys!! You both cleared that up for me : D

 

[Mohammad Moaz]

It's not a typo.

cos30 = .86
cos45= .71
cos60=.5

sin30 = .5
sin45 = .71
sin60=.86

For Rx to be smaller than Ry, the angle must be less than 45 degrees. If you don't understand why, do some quick math. As you said, Rx=Rcostheta and Ry=Rsintheta.

If theta is 60 (bigger than 45) Rx < Ry
If theta is 30 (smaller than 45) Rx > Ry

Excuse me tell me is it possible that theta is equal to Rx /Ry