During a rainy day, rain is falling vertically with a velocity `2 ms^-1`. A boy at rest starts his motion with a constant acceleration of `2 ms^-2` along a straight road. Find the rate at which the angle of the axis of umbrella with vertical should be changed so that the rain always falls parallel to the axis of the umbrella.

Answer

A, B, D

Explanation

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))`