Correct Answer - A::B::D
At any time `t`, rain will appear to the boy as shown in picture.
`tan theta=(at)/(v)`
Boy should hold his unbrella at an angle `theta `from the vertical
`:. tan theta =(at)/(v) sec ^(2) theta(d theta)/(dt)=(a)/(v)`
`rArr (dtheta)/(dt)=(a)/(vsec^(2)theta)=(a)/(v[1+tan^(2)theta])`
`=(a)/(v[1+(a^(2)t^(2))/(v^(2)]])=(av)/(v^(2)+a^(2)t^(2))=(2xx2)/(1+t^(2))`
`(d theta)/(dt)=(1)/(1+t^(2)) ` `Ans. ( d theta)/(dt)=(1)/(1+t^(2))`