Question

A apartie undergoes two displacement.The one has amagnitude of 150cm and makes an angle of 120 degrees with that positive x-axis.The resultant of the two displacement is 140cm at 35 degrees to the positive x-axis .Find the magnitude and direction of second displacement

Answer 1

A = 150 cm at 120 degc

Where A + B = C find B

B = C - A add -A to both sides

Ax = 150 cos 60 = -75

Ay = 150 sin 60 = 129.9

Likewise

Cx = 114.7

Cy = 80.3

Bx = Cx - Ax = 114.7 + 75 = 189.7

By = Cy - Ay = 80.3 -129.9 = -49.6

B = (189.7^2 + 49.6^2)^1/2 = 196.7 length of B vector

tan B = By / Bx = -49.6 / 189.7 B = -14.65 deg

Also

sin B = By / B = -49.6 / 196.1 = -14.65 deg

So B is 196.1 cm at -14.65 deg