Question

the sum of the magnitude of two forces acting a point is 18 and the magnitude of their resultant is 12.if the resultant is at 900 with the forces of smaller magnitude,what are the magnitudes of forces
A)5,13
B)6,12
C)7,11
D)8,10​

Answer 1

Answer:

5,13

Explanation:

Given The sum of the magnitude of two forces acting a point is 18 and the magnitude of their resultant is 12.if the resultant is at 900 with the forces of smaller magnitude,what are the magnitudes of forces  

Let t he force of smaller magnitude be A and force of larger magnitude be B

Now resultant force will be 90 degree

So B will form the hypotenuse.

R^2 = B^2 – A^2

        = 12^2

       = 144

B^2 – A^2 = 144 -----------1

According to question  

A + B = 18

B = 18 - A

Substituting in 1 we get

(18 – A)^2 – A^2 = 144

324 + A^2 – 2(18) A – A^2 = 144

324 – 36 A = 144

36 A = 324 – 144

A = 180 / 36

A = 5

So B = 18 – 5 = 13

Hence the magnitude of the two vectors are (5, 13)