The document addresses a problem involving four displacement vectors with given magnitudes and angles. It provides a detailed calculation of the resultant vector's magnitude and direction, concluding that the resultant angle is 231 degrees. The calculations include breaking down each vector into components and applying vector addition principles.

1. Physics Helpline
L K Satapathy Vectors QA 1
Vectors in a plane
A B
C
D
20
35 50

2. Physics Helpline
L K Satapathy
Answer :
Vectors QA 1
Question by Stephanie : Four displacement vectors A ,
B , C and D are as shown in the diagram. Their
magnitudes are A = 14.6m , B = 11.0m , C = 12.0m
and D = 24.5m . Find the magnitude and direction of
the resultant vector.
(1) : A = 14.6m
A B
C
D
20
35 50
A
20
xA
yA
cos20 14.6 0.9397 13.72 ( )o
xA A m    
sin 20 14.6 0.342 4.99 ( )o
yA A m    
(2) : B = 11.0m (upwards) 0 & 11.0 ( )x yB B m   
(3) : C = 12.0m
cos35 12.0 0.8192 9.83 ( )o
xC C m    
sin35 12.0 0.5736 6.88 ( )o
yC C m    
(4) : D = 24.5m cos50 24.5 0.6428 15.75 ( )o
xD D m    
sin50 24.5 0.766 18.77 ( )o
yD D m    
C
35
xC
yC
D
50 xD
yD

3. Physics Helpline
L K Satapathy Vectors QA 1
Convention : x is +ve to right & y is +ve upward
13.72 9.83 0 15.75 7.80
x x x xX A B C D
m
   
      
4.99 11.0 6.88 18.77 9.66 9.66
y y y yY A B C D
m
   
      ;
Resultant magnitude :
2 2
(7.80) (9.66) 60.84 93.32
154.16 12.42 [ ]
R
A sm n
   
 
7.80m
9.66m
OP
QR

Resultant Direction :
9.66
tan 1.2385 51
7.8
o
    ;
 The required angle = 180 + 51 = 231 [Ans] R
231

4. Physics Helpline
L K Satapathy
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