Problema Solution
Two workers are trying to move a heavy crate. One pushes on the crate with a force , which has a magnitude of 536 newtons (N) and is directed due west. The other pushes with a force , which has a magnitude of 282 N and is directed due north. What are (a) the magnitude and (b) direction of the resultant force + applied to the crate? Suppose that the second worker applies a force - instead of . What then are (c) the magnitude and (d) direction of the resultant force - applied to the crate? In both cases express the direction as a positive angle relative to due west.
Answer provided by our tutors
this is a right triangle problem, we take 536 to be the 'side adjacent', 282 to be the 'side opposite' and we are solving for the a) hypotenuse and b) measure of the angle
let 'm' represent the magnitude of the resultant force:
m^2 = 536^2 + 282^2
solving for 'm' we have m=605.6
let 'a' represent the direction of the force:
tan(a) = 282/536
atan(282/536) = a = 27.8
a force of approximately 606 N is applied at an angle 27.8 degrees west of due north
if the force is applied to the east instead of the west the magnitude stays the same but the resultant force is applied 27.8 degrees east of due north