Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 201912 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 12 April
Shift: Morning Shift
Subject: Physics
Chapter: Motion in Two Dimensions

JEE Main 2019 · 12 April · Morning Shift · Physics · Motion in Two Dimensions

The trajectory of a projectile near the surface of the earth is...

The trajectory of a projectile near the surface of the earth is given as

y = 2x - 9{x}^{2} .

If it were launched at an angle

{\theta}_{0}

with speed

{v}_{0}

then \left(g = 10{ms}^{- 2}\right):

Options

A{\theta}_{0} = \cos^{- 1} $\left(\dfrac{1}{\sqrt{5}}\right)$ and ${v}_{0} = \dfrac{5}{3}m{s}^{- 1}$
B{\theta}_{0} = \cos^{- 1} $\left(\dfrac{2}{\sqrt{5}}\right)$ and ${v}_{0} = \dfrac{3}{5}m{s}^{- 1}$
C{\theta}_{0} = \sin^{- 1} $\left(\dfrac{1}{\sqrt{5}}\right)$ and ${v}_{0} = \dfrac{5}{3}m{s}^{- 1}$
D{\theta}_{0} = \sin^{- 1} $\left(\dfrac{2}{\sqrt{5}}\right)$ and ${v}_{0} = \dfrac{3}{5}m{s}^{- 1}$

Correct answer

A. {\theta}_{0} = \cos^{- 1} $\left(\dfrac{1}{\sqrt{5}}\right)$ and ${v}_{0} = \dfrac{5}{3}m{s}^{- 1}$

Step-by-step solution

y = 2x - 9{x}^{2}

Comparing above equation with general equation of trajectory of projectile

y = xtan \theta\left(1 - \dfrac{x}{R}\right)

tan\theta = 2

⇒ sin\theta = \dfrac{2}{\sqrt{5}}

or

cos\theta = \dfrac{1}{\sqrt{5}}

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

or

\theta = \cos^{- 1}\left(\dfrac{1}{\sqrt{5}}\right)

And R = 2/9

R = \dfrac{{{v}_{0}}^{2}\sin 2\theta}{g} = \dfrac{2}{9}

After substituting the value for g and \sin 2θ. We get

{v}_{0} = \dfrac{3}{5}

m/s

Practice Motion in Two Dimensions on Quantrex Academy →

More from Motion in Two Dimensions

A particle is thrown with a speed v from a point O at an angle θ with the horizontal… JEE Advanced 2026 A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is… JEE Main 2026 Two identical bodies, projected with the same speed at two different angles cover the… JEE Main 2026 If x and y coordinates of a projectile as a function of time (t) are given as 24t and… JEE Main 2026 A gun mounted on the ground fires bullets in all directions with same speed. The farthest… JEE Main 2026 Two projectiles are projected with the same initial velocities at the 15^∘ and 30^∘ with… JEE Main 2026 A boy throws a ball into air at 45^ ∘ from the horizontal to land it on a roof of a… JEE Main 2026 An object is projected with kinetic energy K from a point A at an angle 60^ ∘ with the… JEE Main 2026 Full Motion in Two Dimensions list All JEE Main PYQs