Discover the Magnitudes and Angle Between Two Forces: Resultant Forces Homework

[kalupahana]

Homework Statement

The sum of two forces is 24N. There resultant is act right angle to the smaller of the two forces which is 12N. Find the magnitudes of the two forces & the angle between them.

Homework Equations

R² = P² + Q² + 2PQcosΘ

tan α = QsinΘ/ (P+QcosΘ)

The Attempt at a Solution

R² = P² + Q² + 2PQcosΘ

144 = (24-x)² + x² + x(24-x)cosΘ
0 = (2-cosΘ)x² - 24(2-cosΘ)x + 432
cosΘ = 2x² -48x +432/x(x-24) --------- (1)


tan90 = (24-x)sinΘ / [x + (24-x)cosΘ]
cosΘ = x / (x-24) ---------------(2)

from 1 & 2
x2 = 2x² -48x +432
0 = x² -48x +432
(x-12)(x-36) = 0
x = 12 or x = 36

Then both forces are 12N


I got this. But answer given as 15N and 9 N. Please tell me how to reach to this

 

[rl.bhat]

144 = (24-x)^2 + x^2 + x(24-x)cosΘ

The above equation should be

144 = (24-x)^2 + x^2 + 2x(24-x)cosΘ

 

[kalupahana]

thnx, i got it, the answer come