AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A stationary person observes that rain is falling vertically down at 30 kmh^-1. A cyclist is moving up on an inclined plane making an angle 30^o with horizontal at 10 kmh^-1. In which direction should the cyclist hold his umbrella to prevent himself from the rain?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

At an angle $\tan^{- 1} (\frac{3 \sqrt{3}}{5})$ with inclined plane

At an angle $\tan^{- 1} (\frac{3 \sqrt{3}}{5})$ with horizontal

At an angle $\tan^{- 1} (\frac{\sqrt{3}}{7})$ with inclined plane

At an angle $\tan^{- 1} (\frac{\sqrt{3}}{7})$ with vertical

answer is A, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

${\vec{v}}_{r} = - 30 \hat{j}, {\vec{v}}_{m} = \frac{10 \sqrt{3}}{2} \hat{i} + \frac{10}{2} \hat{j}$

$\tan θ = \frac{5 \sqrt{3}}{35} = \frac{\sqrt{3}}{7} \Rightarrow θ = \tan^{- 1} (\frac{\sqrt{3}}{7})$ with vertical

Angle of v_r/m with inclined plane is

$\begin{array}{l} 60^{\circ} - θ = β \\ \tan β = \tan (60^{\circ} - θ) \\ = \frac{\tan 60^{\circ} - \tan θ}{1 + \tan 60^{\circ} \tan θ} \\ = \frac{\sqrt{3} - \sqrt{3} / 7}{1 + \sqrt{3} \cdot \sqrt{3} / 7} = \frac{3 \sqrt{3}}{5} \end{array}$

$\Rightarrow β = \tan^{- 1} (\frac{3 \sqrt{3}}{5})$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!