Question

Two factors whose magnitudes are in the ratio of 3:5, gives a resultant of 35N. If the angle of the inclination is 60 degrees, find the magnitude of each force and give explanation to your answer.

Answer 1

Let first vector = 3x N
2nd vector = 5x N
Angle between two vectors = 60°
we know,
Resultant of two vector A and B is given by
R = √{A² + B² + 2ABcosФ} , here Ф is the angle between them .

So, 35N = √{(3x)² + (5x)² + 2(3x)(5x)cos60°}
⇒35 = √{9x² + 25x² + 15x²}
⇒35 = 7x
⇒ x = 5

Hence, first vector = 3x = 15N
2nd vector = 5x = 5 × 5 = 25N

Answer 2

Hello Dear.

Here is the answer---


Let the magnitudes of the Factors are 3x and 5x respectively.
∴ A (First Factor) = 3x
 B( Second Vector) = 5x

Angle between them(θ) = 60°
Resultant Vector(R) = 35 N.

Now,
∵ R = $\sqrt{ A^{2} + B^{2} + 2AB Cos theta}$
∴ 35 = $\sqrt{ (3x)^{2} + (5x)^{2} + 2(3x)(5x) Cos 60}$
⇒ 35 = $\sqrt{ 9x^{2} + 25x^{2} + 30x^{2} Cos 60}$
⇒ 35 = √49x² 
On Squaring both Sides,
 1225 = 49x² 
x² = 1225/49
x² = 25 
x = √25
x = 5 N.

Now,

Magnitude of First Vector (A) = 3x
 = 3 × 5
 = 15 N.

Magnitude of Second Vector (B) = 5x
 = 5 × 5
 = 25 N.


Hope it helps.