• # question_answer                                   Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the right is 10 m/s. What is the velocity of B when angle $\alpha ={{60}^{o}}$?                                                                                                                                                                 A)                            9.8 m/s      B)                 10 m/s C)                 5.8 m/s                 D)                 17.3 m/s

Let the velocity along x and y axes be ${{v}_{x}}$ and ${{v}_{y}}$ respectively.                 $\therefore {{v}_{x}}=\frac{dx}{dt}and\,{{v}_{y}}=\frac{dy}{dy}$                 From figure,                 $\tan \alpha =\frac{y}{x}$                 $\Rightarrow y=x\tan \alpha$                 Differentiating Eq. (i) w.r.t. $t$, we get                 $\frac{dy}{dt}=\frac{dx}{dt}\tan \alpha$                 $\Rightarrow$               ${{v}_{y}}={{v}_{x}}\tan \alpha$                 Here,  ${{v}_{x}}=10\,m/s\,,\,\alpha ={{60}^{o}}$                 $\therefore {{v}_{y}}=10\,\tan {{60}^{o}}=10\sqrt{3}=17.3\,m/s$