Question

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

Answer 1

We know Result of two forces x and y will be,
R(say)=sqrt( x^2 + y^2 + 2xycos(theta))-------------(1)

Here, Given
let x = 20sqrt(3)N
R= 20N
theta = 30drgree
Then find y

So using formula (1) above we get the value of y.
Hence,
20=sqrt(1200 +y^2 + 60y)

Squaring both side we get
400= 1200 + y^2 + 60y
y^2 + 60y + 800=0 ---------------(2)

Now solve eq. (2) for y;

y^2 + 40y + 20y + 800=0
y(y + 20) + 40(y + 20)=0
(y +20)(y + 40) =0
y =-20, or y = - 40

Hence both value satisfy the resultant eq. Hence Y can be -20N or -40 N!
But force can never be negativr it represt it is in opposite directon.

This is your required Solution.

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Answer 2

Answer:

20 N

Step-by-step explanation:

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