Forces of Magnitude?

Question

Forces of Magnitude of 250 pounds and 130 pounds act on an object at angles 45 degrees and negative 60 degrees, respectively, with the x axis. Find the direction and magnitude of the resultant of these forces

Answer 1

use law of cosine:

x = 250*cos(45)+130*cos(60) =241.8 lbs


y=250*sin(45)-130*sin(60)=64.2 lbs

the resultant vector is
=sqrt(241.8^2+64.2^2)= 250 lbs

and the angle is
tan(th)=64.2/241.8
th= atan(64.2/241.8)=14.9 degrees

Answer 2

First, decompose each force into it's respective x and y components:

x = 250*cos(45)+130*cos(60)

=241.8 lbs


y=250*sin(45)-130*sin(60)

=64.2 lbs

the resultant vector is
=sqrt(241.8^2+64.2^2)
= 250 lbs

and the angle is
tan(th)=64.2/241.8
th= atan(64.2/241.8)
=14.9 degrees

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