- #1
kalupahana
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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