Two particles A and B are located at point `(0m, 50m)` at `t = 0`. The particle A moves withy a constant velocity and the particle B moves on a circle of radius 50 m having centre at origin `(0, 0)` as shown in figure. The pasrticle B has a constant speed `5pi m//s`. What will be the velocity of particle A so that both the pasrticles reach at point `(50m, 0m)` simultaneously.

Options

A. `10sqrt(3)(hati-hatj)m//s`
B. `(5)/(sqrt(3))(hati-hatj)m//s`
C. `10(hati-hatj)m//s`
D. `5(hati-hatj)m//s`

Answer

C

Explanation

Two particles …………
`t_(A)=t_(B) implies (50sqrt(2))/(V_(A)) = (2pi(50))/(4(5pi)) implies 10sqrt(2)m//s`
`vecV_(A) = 10sqrt(2) (hati cos45^(@)+ - hat j sin 45^(@))`
`= 10(hati - hatj)m//s`