A semicircle of radius R = 5m with diameter AD as shown in figure. Two particles 1 and 2 are at points A and B on shown diameter at t = 0 and move along segments AC and BC with constant speeds `u_(1)` and `u_(2)` respectively. Then the value of `(u_(1))/(u_(2))` for both particles to reach point C simultaneously will be :

Options

A. `(5sqrt(2))/(4)m//sec`
B. `(2sqrt(2))/(5)m//sec`
C. `2sqrt(2)m//sec`
D. `sqrt((5)/(4)m//sec`

Answer

D

Explanation

A semicircle ………………..
From geometry `BC = 4m and AC = 2sqrt(5)m` .
`(AC)/(u_(1)) = (BC)/(u_(2)) or (u_(1))/(u_(2)) = (AC)/(BC) = (2sqrt(5))/(4)`