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3.2 , motion in plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
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
    $10$
  • ✓
    $20$
  • C
    $30$
  • D
    $40$
✓

Answer

Correct option: B.
$20$
b
(b) 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 ${v_{rg}} = \frac{{10}}{{\sin 30^\circ }} = 20\,km/hr$

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