Question

Find the resultant of the following vectors:

Vector A = A velocity of 50 m/s acting 300 north of due east

Vector B = A velocity of 30 m/s acting 600 north of due east

Please show work and formulas

Answer 1

A = 50 m/sec, 30 deg North of east

Ax = A*cos theta

Ax = 50*cos 30 deg = 43.30 m/sec

Ay = A*sin theta

Ay = 50*sin 30 deg = 25 m/sec

B = 30 m/sec, 60 deg North of east

Bx = B*cos theta

Bx = 30*cos 60 deg = 15 m/sec

By = B*sin theta

By = 30*sin 60 deg = 25.98 m/sec

Resultant vector will be

R = A + B

R = Ax + Bx + Ay + By

R = (43.30 + 15) i + (25 + 25.98) j

R = 58.30 i + 50.98 j

|R| = sqrt (58.30^2 + 50.98^2)

|R| = 77.44 m/sec

Angle = arctan (50.98/58.30) = 41.17 deg

So,

Vector R = A velocity of 77.44 m/sec acting 41.17 deg north of due east