Question

Three particles start from the origin at the same time, one with a velocity $v_{1}$ along the $x$ -axis, second along the negative $y$ -axis with a velocity $v_{2}$ and third particle moves along the line $x=y$ . The velocity of third particle, so that three may always lie on the same line is :

• A. $\frac{\text{v}_{1} + \text{v}_{2}}{2}$
• B. $\sqrt{\text{v}_{1} + \text{v}_{2}}$
• C. $\frac{\text{v}_{1} \text{v}_{2}}{\text{v}_{1} + \text{v}_{2}}$
• D. $v=\frac{\sqrt{2} \, v_{1} v_{2}}{v_{2} - v_{1}}$

Answer 1

Answer: (D)

Slope of $AC$ line = Slope of $BA$ line
$\frac{\left(\frac{vt}{\sqrt{2}}-0\right)}{\left(\frac{vt}{\sqrt{2}}-v_{1}t\right)}=\frac{0 - \left(- v_{2} t\right)}{\left(v_{1} t - 0\right)} \, $
$v=\frac{\sqrt{2} \, v_{1} v_{2}}{v_{2} - v_{1}}$