Question

Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

sum of x-components= 150cos(30) + 75cos(150)
= 129.90 + (-64.95)
= 64.95

sum of y-components= 150sin(30) + 75sin(150)
= 75+ 37.5
= 112.5
magnitude = \[\sqrt{x ^{2}+y ^{2}}\]
= \[\sqrt{(64.95)^{2}+ (112.5)^{2}}\]
= 129.90
direction = arctan y/x
= arctan 112.5/64.95
= 60.00

final answer = 129.90 pounds,60 degrees

Answer 2

Thank you! @conan.195114