Two forces

Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer.

Correct answer:

Φ =  60.19 °
F =  39.05

Step-by-step explanation:

F1=25 lb F2=30 lb α=10° rad=10° 180π =10° 1803.1415926 =0.17453=π/18 β=100° rad=100° 180π =100° 1803.1415926 =1.74533=5π/9 γ=βα=π/2=90°  F=F1+F2=(x;y) x=F1 cos(α)+F2 cos(β)=25 cos(0.1745)+30 cos(1.7453)19.4107 y=F1 sin(α)+F2 sin(β)=25 sin(0.1745)+30 sin(1.7453)33.8854  Φ1=arctan(xy)=arctan(19.410733.8854)1.0506 rad Φ=Φ1  =Φ1 π180   =1.0506 π180   =60.19  =60.19=60°1140"



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Showing 1 comment:
#
Dr Math
Angle 100-10 = 90° is right , therefore may be some optimization of calculation made. In general it§s calculated OK.

See also vector adding calculator:

https://www.hackmath.net/en/calculator/sum-of-the-two-vectors?a=25&a1=100-10&b=30&submit=Solve

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