Question

Vector A has a magnitude of 7.20 units and makes an angle of 25.0° with the positive x axis. Vector B also has a magnitude of 7.20 units and is directed along the negative x axis. Using graphical methods, find the following.

(a) the vector sum A + B
___units at ___ ° counterclockwise from the positive x axis

(b) the vector difference A - B
__ units at __° counterclockwise from the positive x axis

Answer 1

here

Ax = A cos theta

Ax = 7.2 cos 25

Ax = 6.52 units

Ay = 7.2 sin 25

Ay = 3.04 units

angle made by B with +x axis is 180 deg

so

Bx = B cos 180 = -7.2 units

By = B sin 180 = 7.2 sin 180 = 0

part A :

A + B = (Ax+Bx) i + (Ay + By) j

A+B = (6.52-.72) i + (3.04 + 0) j

A + B = -0.68 i + 3.04 j

magnitude of (A+B)^2 = (-0.68^2) + (3.04)^2

magnitude of (A+B) = 3.11 m

angle of the resultant tan theta = Y/x

tan theta = -0.68/3.04

theta = -12.6 deg

from + axis it is 360-12.6 = 347.4 deg

-----------------------

A -B = (Ax-Bx) i + (Ay - By)

A-B = (6.52-(-7.2) i + (3.04 - 0)

A-B = 13.72 i + 3.04 j

mag of (A-B) = (A-B)^2 = 13.72^2 + 3.04^2

mag of (A-B) = 14.05 m

tan theta = 3.04/13.72

theta = 12.49 deg