Answered

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Can a 20 N force and 40 N force ever produce a resultant with magnitude of 27 N?

Sagot :

Sure ,Let's find angle between forces

  • Vectors be A and B and resultant be R

[tex]\\ \sf\longmapsto R^2=A^2+B^2+2ABcos\theta[/tex]

[tex]\\ \sf\longmapsto 27^2=20^2+40^2+2(20)(40)cos\theta[/tex]

[tex]\\ \sf\longmapsto 729=400+1600+1600cos\theta[/tex]

[tex]\\ \sf\longmapsto 729=2000+1600cos\theta[/tex]

[tex]\\ \sf\longmapsto 1600cos\theta=-271[/tex]

[tex]\\ \sf\longmapsto cos\theta=-0.169[/tex]

[tex]\\ \sf\longmapsto \theta=cos^{-1}(-0.169)[/tex]

[tex]\\ \sf\longmapsto \theta=80.2°[/tex]

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