A man standing on a road hold his umbrella at $30^° $ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\, km/hr$. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be......... $km/hr$
A man standing on a road hold his umbrella at $30^° $ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\, km/hr$. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be......... $km/hr$
$10$
$20$
$30$
$40$
A man standing on a road hold his umbrella at $30^° $ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\, km/hr$. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be......... $km/hr$
When the man is at rest w.r.t. the ground, the rain comes to him at an angle $30^°$ with the vertical. This is the direction of the velocity of raindrops with respect to the ground.
Here ${\overrightarrow {v} _{rg}} = $ velocity of rain with respect to the ground
${\overrightarrow {v} _{mg}} = $ velocity of the man with respect to the ground.
and ${\overrightarrow {v} _{rm}} = $ velocity of the rain with respect to the man,
We have ${\overrightarrow {v} _{rg}} = {\overrightarrow {v} _{rm}} + {\overrightarrow {v} _{mg}}$......$(i)$
Taking horizontal components equation $ (i) $ gives
${v_{rg}}\sin \,30^\circ = {v_{mg}} = 10\,km/hr$
or ${v_{rg}} = \frac{{10}}{{\sin 30^\circ }} = 20\,km/hr$