Question

. The resultant of two forces has magnitude 20 N. One of the forces is of magnitude 20√3 N and makes an angle of 30° with the resultant. Then what is the magnitude of the other force?

Answer 1

Answer:

the handwriting may not be understandable

but the struggle is real

Explanation:

and the ans. is 100% correct

follow me and ♡♡

Answer 2

ANSWER

Let the other Force be of magnitude x and the angle it makes with resultant be θ.

Now, the components of the two vectors along the resultant should be of magnitude of the resultant and the component of these two vectors resolved in the direction perpendicular to resultant should be zero.

In other words, 20  √3cos30^0 +xcosθ=20

which gives, 20√3.$\frac{\sqrt{3} }{2}+xcos$θ=20

or, 30+xcosθ=20, giving xcosθ=−10 --- (1)

Now, resolving in the perpendicular direction, 20√3. sin30^ 0  +xsinθ=0

or, 10 √ 3  +xsinθ=0, giving xsinθ=−10  √3  --- (2)

Squaring and adding (1) and (2), we get:

(xcosθ) ^2 +(xsinθ)^2= x^2=100+300=400 , thus x=20 N