Question

Two forces of 6 N and 8 N act at a point at an angle of 90° With each other . Determine the magnitude and direction of the resultant, force by drawing a vector diagram

Answer 1

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Answer 2

Answer:

The magnitude of the resultant is 10 and the direction of the resultant is 53°.

Explanation:

The force vectors that are given in the question as,

$F_1=6N$

$F_2=8N$

The magnitude of resultant of these vectors is given as,

$R=\sqrt{F^2_1+F^2_2+2F_1F_2cos\theta}$          (1)

By substituting the value of F₁, F₂, and θ=90° in equation (1) we get;

$R=\sqrt{6^2+8^2_2+2\times 6\times 8\times cos90\textdegree}=\sqrt{36+64} =\sqrt{100}=10$      (cos90°=0)

The direction of the resultant vector is given as,

$tan\phi=\frac{F_2sin\theta}{F_1+F_2cos\theta}=\frac{8\times sin90\textdegree}{6+8cos90\textdegree}=\frac{8}{6}=\frac{4}{3}$                       (sin90°=1)

$\phi=53\textdegree$

Hence, the magnitude of the resultant is 10 and the direction of the resultant is 53°.