Question

Two forces F1=3i+bj and F2=9i+12j act on the same object (i and j are unit vectors along the positive x and y axes).For what value of b will the magnitude of resultant force be minimum

Answer 1

Given: Two forces F1 = 3i + bj and F2 = 9i + 12j

To find: For what value of b will the magnitude of resultant force be minimum?

Solution:

• Now we have given two forces, which act on the same object (i and j are unit vectors along the positive x and y axes).

• So, let R be the resultant force , then:

                      R = F1 + F2

                      R = 3i + bj + 9i + 12j

                      R = 12i + (b + 12)j

• Now calculate magnitude , we get:

                      R = √( 12^2 + (b + 12)^2 )

                       R = √( 144 + (b + 12)^2 )

• Now the  the quantity in root is positive. So, value of b will minimize 144 + (b + 12)^2 and will also minimize R the magnitude .

• So: 144 + (b + 12)^2, b can take -12 value.

Answer:

            So the value of b is -12.