Question
A person standing on a road has to hold his umbrella at 300 with the vertical to keep the rain away. He throws the umbrella and starts running at 10 m/s. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to,
a) the road,
b) the moving person.
Solution
When a person is at rest with respect to ground, the rain is coming to him at an angle 30o with the vertical, i.e., along OB.
As the person moves along OA with velocity 10 m/s, the relative velocity of rain w.r.t person is along OC as shown in fig. below.
Here, o
Therefore, velocity of rain w.r.t ground = 
Velocity of person w.r.t. ground = 
Velocity of rain w.r.t person = 
a) 
b)
In 
= 10/ (1/
) = 10
Therefore, velocity of train w.r.t person = 10
m/s
