Direction & Magnitude of Resultant Forces

[nycmathguy]

Section 6.3

Please, do 81 in step by step fashion.
Thank you.

 

[MathLover1]

81.

V1= 75(cos(30)°,sin(30)°
V2=100(cos(45)°,sin(45)°)
V3=125(cos(120),sin(120))

The usual method is to resolve each force into a component along the x axis and another along the y axis.
Add up the components. Then compound them back together.

So for the x components:
Rx = 75cos(30° )+ 100cos(45°) + 125cos(120°)=73.163

For the y components:
Ry = 75sin(30)° + 100sin(45) + 125sin(120°)=179.618

Then resultant R= sqrt( (R[x])^2 +( R[y])^2)

R= sqrt( (73.163)^2 +( 179.618)^2)

R= 193.947

At angle inv tan(alpha)= (Ry/Rx)

tan(alpha)=179.618 /73.163
tan(alpha)=2.455038749094488
alpha=tan^-1(2.455038749094488)
alpha=1.1839908188921035...(result in radians)
alpha=67.84°

 

[nycmathguy]

81.
View attachment 1823

V1= 75(cos(30)°,sin(30)°
V2=100(cos(45)°,sin(45)°)
V3=125(cos(120),sin(120))

The usual method is to resolve each force into a component along the x axis and another along the y axis.
Add up the components. Then compound them back together.

So for the x components:
Rx = 75cos(30° )+ 100cos(45°) + 125cos(120°)=73.163

For the y components:
Ry = 75sin(30)° + 100sin(45) + 125sin(120°)=179.618

Then resultant R= sqrt( (R[x])^2 +( R[y])^2)

R= sqrt( (73.163)^2 +( 179.618)^2)

R= 193.947

At angle inv tan(alpha)= (Ry/Rx)

tan(alpha)=179.618 /73.163
tan(alpha)=2.455038749094488
alpha=tan^-1(2.455038749094488)
alpha=1.1839908188921035...(result in radians)
alpha=67.84°

Thank you for your patience.
Thank you for being who you are.
Thank you for all the math help you have given me since we met last year.