Three particles start from the origin at the same time, one with velocity `u_1` along the x-axis, the second with velocity `u_2` along the y-axis . Find the velocity of the third particles, along the x=y line so that the three particles may always lie on the same straight line.

Options

A. `(u_(1)+u_(2))/(2)`
B. `sqrt(u_(1)u_(2))`
C. `(u_(1)u_(2))/(u_(1)+u_(2))`
D. `(sqrt(2)u_(1)u_(2))/(u_(1)+u_(2))`

Answer

D

Explanation

OA =x=`u_(1)t`
` OB =y=u_(2)=u_(2)t`
`OC = u^(2)`
from intercept from of eq of use
`(x)/(a)+(y)/(b)=1`
`(ut cos 45^(@))/(u_(1)t)+(ut sin 45^(@))/(u_(2)t)=1`
After solving we get
` v= (sqrt(2)u_(1)u_(2))/(u_(1)+u_(2))`