Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown. The velocity of A to the left is 10 `ms^(-1)` What is the velocity of B when angle`alpha=60^(@)`?

Options

A. 9.8 m`s^(-1)`
B. 10 m`s^(-1)`
C. 5.8 m`s^(-1)`
D. 17.3 m`s^(-1)`

Answer

c

Explanation

Speed of A =`(dx)/(dt)=10 m s^(-1)`
Speed of `B =dy//dt`
Now `x^(2)+y^(2)=(AB)^(2)` Diff. w.r.t. t

`2x(dx)/(dt)+2ydy//dt=0`
or`(dy)/(dt) =- (x)/(y)(dx)/(dt)= - cot 60^(@)xx10 = - 5.8 ms^(-1)`