Q27E - University Physics with Modern Physics

Question

Compute the x- and y-components of the vectors $\stackrel{\rightharpoonup }{A}$,$\stackrel{\rightharpoonup }{B}$, $\stackrel{\rightharpoonup }{C}$ and $\stackrel{\rightharpoonup }{D}$ in Fig. E1.24.

                                           

Step-by-Step Solution

Answer

The x and the y components of vector  A, B, C and D are  (0,-8) ; (7.5 , 13); (-10.88,-5.07) and (-7.99, 6.02) respectively ,

Step 1: Representation of vector

Here,

 Vector are easily defined with the help of there magnitude and there angle with the x and the y axes. 

Here in this case there are four vectors given 

For this vector we will take the use of magnitude given as well as the angle with the x axis and the y axis. 

Step 2: Conversion of mile into kilometer

For the direction shown in the graph 

 $\stackrel{\rightharpoonup }{A}$ =(0, -8)  in meters

As here the vector is exactly on the y axis so the magnitude with respect to y axis will be zero.

For vector B the angle of that vector made with the x axis will be  90 – 30 

That is the angle made will be 60 

Hence the components of the b vector will be  magnitude multiplied by the cos angle and sin angle made with respect to x axis 

$\stackrel{\rightharpoonup }{B}=15 \cos 60+15 \sin 60$ 

By putting the value of cos 60 = ½ and sin 60 = $\sqrt{3}$ /2 

We get 

  $\stackrel{\rightharpoonup }{B}$= (7.5 , 13) in meters

 

Similarly for vector C