Two particle are moing along `X` and `Y` axes towards the origin with constant speeds `u` and `v` respectively. At time `t=0`, their repective distance from the origin are `x` and `y`. The time instant at which the particles will be closest to each other is

Options

A. `sqrt(x^(2)+y^(2))/sqrt(u^(2)+v^(2))`
B. `(vx+uy)/(u^(2)+v^(2))`
C. `(ux+vy)/(u^(2)+v^(2))`
D. `(2sqrt(x^(2)+y^(2)))/(u+v)`

Answer

C

Explanation

`sqrt(x^(2)+y^(2))cos(theta_(1)-theta_(2))=(sqrt(v^(2)+u^(2)))t`
`rArrt=(sqrt(x^(2)+y^(2)))/(sqrt(v^(2)+u^(2)))[(vy+ux)/(sqrt(x^(2)+y^(2'))sqrt(v^(2)+u^(2)))]=(ux+vy)/(u^(2)+v^(2))`