Question

A man standing on the road has to hold his umbrella at 30° with the vertical to keep the rain away. He throws away the umbrella and starts, running at 10 km/h and finds raindrops hitting his head vertically. The speed of the raindrops with respect to the road is ______.

Options

• 20 km/h

• 10 km/h

• `10sqrt3` km/h

• `10//sqrt3` km/h

Answer 1

A man standing on the road has to hold his umbrella at 30° with the vertical to keep the rain away. He throws away the umbrella and starts, running at 10 km/h and finds raindrops hitting his head vertically. The speed of the raindrops with respect to the road is 20 km/h.

Explanation:

Let velocity of rain be `bar"V"_"r" = "a"hat"i" - "b"hat"j"`

Velocity of rain w.r.t man

`"V"_"rm" = bar"V"_"r" - bar"V"_"m" = 10hat"i"`

`= "a"hat"i" - "b"hat"j" - 10hat"i"`

`= ("a" - 10)hat"i" - "b"hat"j"`

a - 10 = 0 as V_rm in vertical

a = 10

Also, V_r sin 60° = a = 10

`therefore "V"_"r"/2 = 10`

`=> "V"_"r"` = 20 km/hr