Three particles start from origin at the same time: one with velocity `v^(1)` along positive x-axis, the second along the positive y-axis with a velocity `v^(2)` and the third along the line y = x with such a speed that all the three always stay in a straight line, then velocity of the third particles is:

Options

A. `sqrt(v_(1) v_(2))`
B. `(v_(1) + v_(2))/(2)`
C. `(v_(1) v_(2))/(sqrt(v_(1)^(2) + v_(2)^(2))`
D. `(v_(1) v_(2) sqrt2)/(v_(1) + v_(2))`

Answer

D

Explanation

`(v_(2)t - (vt)/(sqrt2))/((vt)/(sqrt2)) = ((vt)/(sqrt2))/(v_(1) t - (vt)/(sqrt2))`

`rArr v = (v_(1)v_(2)sqrt2)/(v_(1)+ v_(2))`