Three particles start from origin at the same time with a velocity 2 ms-1 along positive x-axis, the second with a velocity 6 ms-1 along negative y-axis. Find the velocity of the third particle along x = y line so that the three particles may always lie in a straight line.

Question

Three particles start from origin at the same time with a velocity 2 ms-1 along positive x-axis, the second with a velocity 6 ms-1 along negative y-axis. Find the velocity of the third particle along x = y line so that the three particles may always lie in a straight line. (A) -3√3 (B) 3√2 (C) -3√2 (D) 2√2

Tardigrade Admin · Accepted Answer

Slope AB = slope AC <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/384ebced4ce416561012f1d65bcee417-.png" /> (2t - 0/0 + 6t) = (2t - (vt/√2)/0 - (vt)√2) Solve to get v = 3√2 m/s

Q. Three particles start from origin at the same time with a velocity $2 m s^{- 1}$ along positive $x$ -axis, the second with a velocity $6 m s^{- 1}$ along negative $y$ -axis. Find the velocity of the third particle along $x = y$ line so that the three particles may always lie in a straight line.

$- 33$

$32$

$- 32$

$22$

Slope $A B =$ slope $A C$

$\frac{2 t - 0}{0 + 6 t} = \frac{2 t - \frac{v t}{2}}{0 - \frac{v t}{2}}$

Solve to get $v = 32 m / s$

Q. Three particles start from origin at the same time with a velocity 2ms−1 along positive x-axis, the second with a velocity 6ms−1 along negative y-axis. Find the velocity of the third particle along x=y line so that the three particles may always lie in a straight line.

−33​

32​

−32​

22​