Now we’ll use the component method to add two vectors. We will use this techniqu

Question

Now we’ll use the component method to add two vectors. We will use this technique extensively when we begin to consider how forces act upon an object. Vector A  has a magnitude of 50 cm and a direction of 30, and vector B  has a magnitude of 35 cm and a direction of 110. Both angles are measured counterclockwise from the positive x axis. Use components to calculate the magnitude and direction of the vector sum (i.e., the resultant) R =A +B .

PART A

Find the magnitude of the vector sum of these two vectors by using components: 65 m , 65 ; 70 m , 125 .

Express the magnitude in meters to the nearest integer.

PART B

Find the direction of the vector sum of these two vectors by using components: 65 m , 65 ; 70 m , 125 .

Express the direction in degrees as an integer.

Explanation / Answer

Part A

Ax = 65 cos 65o = 27.47m

Ay = 65 sin 65o  = 58.9m

Bx = 70 cos 125o = -40.2 m

By = 70 sin125o = 57.3 m

if R is the resultant of the two vectors

Rx = Ax+Bx = -12.73

Ry = Ay +By = 116.2m

magnitude of R is given by

llR ll = (Rx2 +Ry2)1/2 = 116.89 m= 117m

Part B

tan x = Ry/Rx =116.2/-12.73

=> 96o

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