An open merry go round rotates at an angular velocity `omega`.A person stands in it at a distance `r` from the rotational axis.It is raining and the rain drops falls vertically at a velocity `v_(0)`.How should the person hold an umbrella to protect himself from the rain in the best way.Angle made by umbrella with the vertical is

Options

A. `cot alpha=(v_(0))/(romega)`
B. `tan alpha=(v_(0))/(romega)`
C. `cot alpha=(romega)/(v_(0))`
D. `tan alpha=(v_(0))/(romega)`

Answer

a

Explanation

Let the velocity of the drops above the preson rel. to the merry go round be at an angle `alpha` to the vertical. This angle can be determined from the velocity triangle `v_(0)=v_("rel")+v_(m.g.r.)`,
`v_("rel")=v_(0)-v_(m.g.r)`
`v_(m.g.r)=romega, cot alpha=(v_(0))/(romega)`