Rank the cases from greatest to smallest in order of magnitude

[Rijad Hadzic]

Homework Statement

http://imgur.com/PUrHBaa
Question 13 in the middle of the page.

Each case in the figure shows an example of force vectors exerted on an object. These forces are all of the same magnitude F_o. Assume the forces lie in the plane of the paper. Rank the cases from greatest to smallest in order of magnitude of the total force. Note: the total force is the vector sum of the individual forces exerted on the objct.

Homework Equations

The Attempt at a Solution

Okay so they say they all have the same magnitude, so I chose value 1 for F_o just to make it simple.

That gives me a magnitude of 1 for case C.

For case B, you have F_y = 1 + sin (5deg) and F_x = cos (5 deg). using (a^2 + b^2 )^(1/2) you get 1.47 N

For case A you have F_y = 1 - sin (5 deg) and F_x = cos (5 deg). Using (a^2 + b^2 )^(1/2) you get 1.35 N

but my book tells me the answer is B>C>A

Is my book just wrong? Or am I doing this wrong? This is simple pythagorean theorem..

 

[haruspex]

my book tells me the answer is B>C>A

Your book is wrong. Not until the angle is increased from 5 degrees to 30 degrees would the net force in A have as low a magnitude as |F_o|.

 

[Rijad Hadzic]

Your book is wrong. Not until the angle is increased from 5 degrees to 30 degrees would the net force in A have as low a magnitude as |F_o|.

Man I am not sure if I should just throw this book away or not now lol. I think there are some problems in the early chapters but jts better in the late chapters for some reason.. I already took this course but I am going back and strengthening my knowledge..