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JEE Main 202227 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
27 June
Shift
Morning Shift
Subject
Physics
Chapter
Motion in Two Dimensions

JEE Main 2022 · 27 June · Morning Shift · Physics · Motion in Two Dimensions

A girl standing on road holds her umbrella at 45 ° with the...

A girl standing on road holds her umbrella at 45°45 ° with the vertical to keep the rain away. If she starts running without umbrella with a speed of 152kmh−115\sqrt{2}km{h}^{- 1}, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl isA girl standing on road holds her umbrella at 45 ° with the vertical to keep the rain away. If she starts runningA girl standing on road holds her umbrella at 45 ° with the vertical to keep the rain away. If she starts running

Options

  1. A30kmh−130km{h}^{- 1}
  2. B252kmh−1\dfrac{25}{\sqrt{2}}km{h}^{- 1}
  3. C302kmh−1\dfrac{30}{\sqrt{2}}km{h}^{- 1}
  4. D25kmh−125km{h}^{- 1}

Correct answer

C. 302kmh−1\dfrac{30}{\sqrt{2}}km{h}^{- 1}

Step-by-step solution

A girl standing on road holds her umbrella at 45 ° with the vertical to keep the rain away. If she starts running

v→rg=v→r−v→g\overset{\to}{v}rg = \overset{\to}{v}r - \overset{\to}{v}g

A girl standing on road holds her umbrella at 45 ° with the vertical to keep the rain away. If she starts running

From the above diagram, velocity of the raindrop wrt ground will be,

∣v→r∣=(152)2+(152)2=30kmh−1\left|\overset{\to}{v}r\right| = \sqrt{{\left(15\sqrt{2}\right)}^{2} + {\left(15\sqrt{2}\right)}^{2}} = 30km{h}^{- 1}

And velocity of the raindrop wrt the moving girl will be,

\left|\overset{\to}{v}rg\right| = 15\sqrt{2} = \dfrac{30}{\sqrt{2}}km{h}^{- 1}

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