#### Question

# Physics question about vectors?

i still dont get this problem.. no one has yet to explain in detail how to answer this problem so i am still lost! help pleasee! if you can please show your work in steps and then where the answer is.

Three vectors are shown in Fig. 3-32 (A = 70.0 , B = 58.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors.

Figure 3-32:

http://www.webassign.net/giancoli5/3_35alt.gif

a) Give the resultant in terms of components.

Rx = ____________

Ry = ____________

(b) What is the magnitude of the resultant?

____________

What is the resultant's angle above the +x axis?

____________°

The lines mean thats where the answer goes

#### Answers

ok so the easiest way to do this is to break up all the vectors into x and y components (horizontal and vertical)

B breaks up like this:

40cos(58) = 21.1967 to the left

40sin(58) = 33.921924 upwards

......................................…

A: 70cos(28) = 61.80633 to the right

70sin(28) = 32.863 upwards

......................................…

C: since c does not have a horizontal component, its already ready to be added. its angle is 90 whose sin = 1.

46.8sin(90) = 46.8 downwards

......................................…

now, add up all the horizontal and vertical components

make all the vectors to the left negative, and to the right positive

and all the vectors upwards positive, and downwards negative

so horizontally you get :

-21.1967 + 61.80633 = 40.6093

since 40.6093 turns out to be positive, it is pointing to the right

......................................…

vertically:

32.863 + 33.921924 - 46.8 = 19.985

19.985 is also positive, so it points up

......................................…

so the resultant in terms of Rx and Ry (components) is:

Rx = 40.60963

Ry = 19.985

......................................…

the magnitude uses the pythagorean theorem

sqrt[ (40.60963)^2 + (19.985)^2 ] = 45.2608

......................................…

the angle of the resultant is

arctan( 19.985 / 40.60963 ) = 26.203

the reason u do arctan is b/c its opposite over adjacent. if you were to draw the resultant vector, you would start at the origin, go to the right 40.60963 units, and upwards 19.9985, and draw a diagonal line up and to the right. the vector is going to be more towards the right than it is upwards, which will give you a pretty small angle, 26.203