Question

Two horizontal forces act on an object. One force has a magnitude of 75.0 N and is directed due 30.0° south of east. The other force has a magnitude of 55.0 N and is directed due 70.0° north of west. What is the magnitude and direction of the sum of the two force vectors. Select one: 122.4 N, 43.2° north of east 130.0 N, 40.0° south of east 46.6 N, 17.1° south of east 48.3 N, 17.1° north of east 20.0 N, 40.0° north of east

Answer 1

Step-by-step explanation:

70 degrees North of west = 110 degrees

30 degrees southof east = - 30 degrees:

Vertical components added together =

75 (sin -30) + 55 sin 110 = 14.18 N

Horizontal components added together =

75 cos (-30) + 55 cos 110 = 46.14 N

Magnitude = sqrt ( 14.18^2 + 46.14^2 ) = 48.3 N

direction = arctan ( 14.18 / 46.14) = ~ 17.1 North of East