Question

In the figure shown, find out the value of theta at this instant (assume string to be tight]
(A)tan^(-1) 3/4
(B)tan^(-1) 4/3
(C)tan^(-1) 3/8
(D) NONE OF THESE

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Answer 1

Given: Velocity of black A is 3.25m/s and of B is √3 m/s

To find:  The value of theta at this instant=?

Solution:

• In this question, we first need to divide all the components in the form of sin Ф and cos Ф.
• At A to the fixed point = 3.25 cos Ф
• At fixed point to B = √3 cos 30°
• In opposite direction of B to fixed point = 1 x cos 60°
• In opposite direction of A to the fixed point = 1 x sin Ф
• So, now adding all the components, we get:

               √3 cos 30° + 1 x cos 60° + 1 x sin Ф = 13/4 cos Ф

                3/2 + 1/2 + sin Ф = 13/4 cos Ф

                2 + sin Ф = 13/4 cos Ф

                8 +  4 sin Ф = 13 cos Ф

                4 sin Ф - 13 cos Ф = -8

• Now, lets consider first option,

             tan (^-1) 3/4 = Ф

             tan Ф = 3/4

• So, sin Ф = 3/5 and cos Ф = 4/5
• putting these values we get:

              4 x 3/5 - 13 x 4/5 = -8

             12/5 - 52/5 = -8

             -40/5 = -8

             -8 = -8

• Hence first option is correct.

Answer:

                The value of theta at this instant is (A) tan^(-1) 3/4