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 cosα+F2 cosβ=25 cos0.1745+30 cos1.745319.4107 y=F1 sinα+F2 sinβ=25 sin0.1745+30 sin1.745333.8854  Φ1=arctan(xy)=arctan(19.410733.8854)1.0506 rad Φ=Φ1  °=Φ1 π180   °=1.0506 π180   °=60.19  °=60.19=60°1140"
F2=x2+y2 F=x2+y2=19.41072+33.88542=5 6139.0512   Verifying Solution:  F2=F12+F22=252+39.05122=5 6139.0512



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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





Tips for related online calculators
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
See also our right triangle calculator.
Do you want to round the number?
See also our trigonometric triangle calculator.

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