Question

Two forces are in the ratio of 3:5 give a resultant of 35N. If the angle of inclination be 60°, calculate the magnitude of each force.

Answer 1

Let the 2 vectors have magnitudes 3x and 5x respectively. Then by parallelogram law,

R² = A² + B² + 2ABcosθ

Ie,35² = (3x)² + (5x)² + 2(3x)(5x)cos60˚

ie 1225 = 9x² + 25x² + 30x²(1/2)

ie 1225 = 34x² + 15x²

ie 1225 = 49x²
x² = 25
x = 5

So magnitude of first vector is 3x which is equal to 15N and that of the second vector is 5x which equals 25N.