Question

Three particles start moving simultaneously from a point on a horizontal smooth plane. First particle moves with speed v₁ towards east, second particle moves towards north with speed v₂ and third one moves towards north east. The velocity of the third particle, so that the three always lie on a straight line, is

• A. $\frac{v_{1} + v_{2}}{2}$
• B. $\sqrt{v_{1}v_{2}}$s
• C. $\frac{v_{1}v_{2}}{v_{1} + v_{2}}$
• D. $\sqrt{2}\frac{v_{1}v_{2}}{v_{1} + v_{2}}$

Answer 1

Answer: (D)

$\sqrt{2}\frac{v_{1}v_{2}}{v_{1} + v_{2}}$

Answer 2

using $\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{y_{1} - y_{3}}{x_{1} - x_{3}},$ we have

$\frac{v_{2}t - 0}{0 - v_{1}t} = \frac{0 - \left( v_{3}/\sqrt{2} \right)t}{v_{1}t - \left( v_{3}/\sqrt{2} \right)t}$

⇒ v₃ = $\frac{\sqrt{2}v_{1}v_{2}}{v_{1} + v_{2}}$,

Hence (4) is correct.