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Find the magnitude of two forces having their resultant 12N which is perpendicular to the smaller force and their greatest resultant is 18N.

Find the magnitude of two forces having their resultant 12N which is perpendicular to the smaller force and their greatest resultant is 18N.

Grade:12th pass

1 Answers

Pratyush Ranjan
11 Points
5 years ago
Let the two vectors be a and b.We get the greatest resultant when the angle between the two vectors is 0°.So a+b=18 Let the resultant be perpendicular to a therefore a + component of b along a is zero. If the angle between a and b is x, then b.cosx + a=0. --------iBy drawing the figure of a,b and their resultant we can show that b.cos(x-90°)=12 or b.sinx=12. --------iiBy squaring the equation ii we get b.cosx =√[b^2-144]From ib.cosx + a =0 or√[b^2-144] + 18-b=0orb^2-144=[18-b]^2Solving the equation we get b=5. .°. a = 18-5=13

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