Force of 90lb acts on An object at an angle of 55 degrees. A 2nd force of 100lbs acts in object at angle of -60 degrees. Find direction & magnitude of force

Question

Need help on this please

Answer 1

We must break each force down into it's x and y components, add them together, and then convert back to polar coordinates.

 

Force 1: x=90cos 55 = 51.62  y=90sin 55 = 73.72

 

Force 2: x=100cos 300 = 50   y=100sin300 = -86.60  (300 degrees equals -60 degrees)

 

Combined Force:  x= 101.62  y = -12.88

 

Magnitude = sqrt(101.62² + 12.88²) = 102.43

 

Angle = InvTan(-12.88/101.62) = -7.22 = 352.78 degrees