Question

The resultant of two equal force acting at right angle to each other is 1414 N.What is the maginitude of each vector?

Answer 1

The resultant of two forces( say a and b )is given by the formula, R=√(a^2 +b^2 +2ab cos β)

Where β is the angle between the two forces

Here, β=90°

And a=b, since the two forces are equal

So, R=√(a^2 + a^2 +2a x a x cos 90)

Cos 90=0.

So R=√(2a^2)=√2 a

BTP,

1414=√2 a

a=1414/1.414[√2=1.414]

a=1000 N. (Ans)

So, the magnitude of each force =1000N.

Hope so it is helpful.!