Find the resultant vector by adding the following vectors: 250m 10o West of South and 455m 26o North of East

Question

Find the resultant vector by adding the following vectors:
250m 10o West of South and 455m 26o North of East

 

Thank you!

Answer 1

If I could draw the figure for you, it would be easy to explain and get

the answer

 

1) Draw the two vectors stated;  Use the arrows depicting East and

    South in terms of direction

 

    a) draw a vector above the East arrow that forms a 26° angle with

        the East arrow, label that vector 455m

 

    b) draw a vector to the left of the South arrow that forms a

        10° angle with the South arrow, label that vector 250m

 

2) Your resultant vector will be the diagonal of the parallelogram which

    has these two vectors as two consecutive sides

 

3) the angle between the two vectors you have drawn is 

    26° + 90° + 10° = 126°

 

Remember: Opposite sides of a parallelogram are equal;

                     Consecutive angles of a parallelogram are

                     supplementary

 

You could use Law of Cosines to find the diagonal or you could do a 

couple more things and then use Law of Sines

 

Answer 2

Draw the first vector; it has angle 260^o, measuring from 0 degrees = due East, in the classic positive counterclockwise fashion conventional in Trig. functions. Ten degrees west of south has angle 260 degrees; 26 degrees north of east has angle 26 degrees.

 

Write each vector in terms of its components:

 

V₁ = ‹250cos 260, 250sin260› = <-43.412, -246.202>

 

similarly, v₂ = ‹455cos 26, 455sin26› = 455408.951, 199.459>

 

Theresultant vector has component form <x₁+x_2, y₁+y₂> which means YOU just add the above x components and the above y components.

 

As always, check the work!