The magnitude of the resultant `vec R` of two forces `vec P and vec Q" is 20 N. "vec R` make an angle of `30^(@)` with `vec P` and an angle of `60^(@)` with `vec Q`. What are the magnitudes of `vec P and vec Q` ?

Options

A. `P=10 N, Q =10 sqrt(3) N`
B. `P=10sqrt(3) N, Q=20 N`
C. `P=20 N, Q=20 sqrt(3) N`
D. `P=10 sqrt(3) N, Q=10 N`

Answer

D

Explanation

From the figure we find that `vec P` is perpendicular to `vec Q` and tan 60^(@) =(P)/(Q)`
`therefore sqrt (3) =(P)/(Q) therefore P= sqrt(3)Q therefore P^(2)=3Q^(2) and because R^(2) =P^(2) +Q^(2) therefoer 20^(2) =3Q^(2) +Q^(2)`
`4Q^(2)=400 therefore Q =10 N and P= sqrt (3) Q =10 sqrt (3) N`