The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90o with the force of smaller magnitude, what are the magnitudes of forces?

A
12, 5
B
14, 4
C
5, 13
D
10, 8

Solution:

Let P be the smaller force and Q be the greater force, then according to the problem

$\begin{array}{l} P + Q = 18 . . . . . . . . . . . . . . . . . . (i) \end{array}$

$P^{2} + R^{2} = Q^{2}$

$\Rightarrow R^{2} = Q^{2} - P^{2}$

$\Rightarrow 12^{2} = (Q - P) (Q + P)$

$\Rightarrow 144 = (Q - P) 18$

$\Rightarrow (Q - P) = 8 - - - - (2)$

$\begin{array}{l} f r o m (1) & (2) w e g e t \\ Q + P = 18 \\ Q - P = 8 \\ _______ \\ 2 Q = 26 \\ ______ \\ Q = 13 \\ s u b s t i t u t e i n (1) w e g e t \\ P = 5 \end{array}$

The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90^o with the force of smaller magnitude, what are the magnitudes of forces?

Solution:

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