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kalupahana

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## Homework Statement

The resultant of two forces P & Q is √3Q. It make angle of 30

^{o}with the direction of force P. Show that P is either equal to Q or equal to 2Q.

## Homework Equations

R

^{2}= P

^{2}+ Q

^{2}+ 2PQcosΘ

tanα = QsinΘ/[P+QcosΘ]

## The Attempt at a Solution

From R

^{2}= P

^{2}+ Q

^{2}+ 2PQcosΘ

3Q

^{2}= P

^{2}+ Q

^{2}+ 2PQcosΘ

2Q

^{2}= P

^{2}+ 2PQcosΘ

4Q

^{2}= P[P+QcosΘ]---------------(1)

From tanα = QsinΘ/[P+QcosΘ]

tan 30 = QsinΘ/[P+QcosΘ]

1/√3 = QsinΘ/[P+QcosΘ]

P+QcosΘ = √3QsinΘ-------------------(2)

replacing 1 with 2

4Q

^{2}=√3 PQsinΘ

PsinΘ = 4/√3

from here what should I do to find the values of P.