Question

The magnitude of resultant of two forces is 10 root 7 N. If the magnitude of one of the forces
is 10 root 3 N and the angle
between two forces is 30°, then the value of second force is 2n. n=?​

Answer 1

Answer:

n=5 and -20

Step-by-step explanation:

Resultant between two vactors is given by

${r}^{2} = {a}^{2} + {b}^{2} + 2ab \cos( \alpha )$

$a = 10 \sqrt{3} \\ \\ r = 10 \sqrt{7} \\ \\ b = 2n \\ \\ \cos( \alpha) = 30 = \frac{ \sqrt{3} }{2} \\ \\ now \: putting \: all \: these \: values \: in \: eqation \\ you \: will \: get \\ \\ (10 \sqrt{7} )^{2} = ( {10 \sqrt{3} )}^{2} + 2n ^{2} + 2 \times 2</strong><strong>n</strong><strong>\times 10 \sqrt{3} \times \ \frac{ \sqrt{3} }{2}$

on factorization

$700 = 300 + 4n^{2} + 60n \\ \\ 4n {}^{2} + 60n - 400 = 0 \\ \\ on \: factorization \\ \\ \\ n(n + 20) - 5(n + 20) = 0 \\ \\ so \\ \\ n = 5 \: \: and \: \: \\ n = - 20$

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