The trajectory of a projectile near the surface of the earth is given as y=2x-9x^{2}. If it were launched at an angle \theta_{0} with speed v_{0} then \left ( g=10ms^{-2} \right ):

  • Option 1)

    \theta_{0}=\sin^{-1}\left ( \frac{2}{\sqrt{5}} \right ) and v_{0}=\frac{3}{5}ms^{-1}

  • Option 2)

    \theta_{0}=\cos^{-1}\left ( \frac{2}{\sqrt{5}} \right ) and v_{0}=\frac{3}{5}ms^{-1}

  • Option 3)

    \theta_{0}=\cos^{-1}\left ( \frac{1}{\sqrt{5}} \right ) and v_{0}=\frac{5}{3}ms^{-1}

  • Option 4)

    \theta_{0}=\sin^{-1}\left ( \frac{1}{\sqrt{5}} \right ) and v_{0}=\frac{5}{3}ms^{-1}

 

Answers (1)

 

Equation of path of a projectile -

y= x \tan \theta\: - \: \frac{gx^{2}}{2u^{2}\cos ^{2}\theta }

it is equation of parabola

g\rightarrow    Acceleratio due to gravity

u\rightarrow    initial velocity

\theta = Angle of projection

 

- wherein

Path followed by a projectile is parabolic is nature.

 

 

Given,      y=2x-9x^{2}

General Eqn.  \rightarrow y= x\tan\theta-\frac{1}{2}\frac{gx^{2}}{v^{2}\cos^{2}\theta}

\Rightarrow \tan\theta=2

\Rightarrow \theta =\sin^{-1}\left ( \frac{2}{\sqrt{5}} \right )=\cos^{-1}\left ( \frac{1}{\sqrt{5}} \right )

\frac{g}{2v^{2}\cos^{2}\theta}=9

\Rightarrow \frac{g}{2v^{2}\times\frac{1}{5}}=9

\Rightarrow \frac{10\times5}{2\times9}=v^{2}

\Rightarrow v^{2}=\frac{25}{9}

v=\frac{5}{3}m/s


Option 1)

\theta_{0}=\sin^{-1}\left ( \frac{2}{\sqrt{5}} \right ) and v_{0}=\frac{3}{5}ms^{-1}

Option 2)

\theta_{0}=\cos^{-1}\left ( \frac{2}{\sqrt{5}} \right ) and v_{0}=\frac{3}{5}ms^{-1}

Option 3)

\theta_{0}=\cos^{-1}\left ( \frac{1}{\sqrt{5}} \right ) and v_{0}=\frac{5}{3}ms^{-1}

Option 4)

\theta_{0}=\sin^{-1}\left ( \frac{1}{\sqrt{5}} \right ) and v_{0}=\frac{5}{3}ms^{-1}

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions