A particle is moving in xy-plane with a constant speed v _ 0 such that its y displacement is given by y= ^ - 2 v _ x 3 v _ 0 , where v_ x is component of velocity along the x-axis. If at some instant x component of it

Correct answer: A. α e^ - 1 Here, particle is moving in two - dimensional (x – y) plane, with constant speed so slope of graph d y d x = v _ y v _ x and& v _ 0 = v _x^ 2 + v _y^ 2 . As slope, dy dx = - 1 3 = v _ y v _ x So, v _ x = - v _ y 3 On squaring and adding v _x^ 2 + v _y^ 2 = v _ 0 ^ 2 3 v_y^ 2 + v _y^ 2 = v _ 0 ^ 2 v _ y = ± v _ 0 2 v _ x = ∓ 3 v _ 0 2 So, y = α e^ - 2 3 v _ 0 × 3 v _ 0 2 y = α e^ - 1

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Motion in Two Dimensions

NTA Abhyas 2020 · Physics · Motion in Two Dimensions

A particle is moving in xy-plane with a constant speed v _ 0 such...

A particle is moving in xy-plane with a constant speed

{v}_{0}

such that its y displacement is given by

\text{y}=\alphae^{\text{-}\dfrac{2{v}_{x}}{\sqrt{3}{v}_{0}}}\text{,}

where v_{x} is component of velocity along the x-axis. If at some instant x component of it velocity is positive and the slope of the tangent on its path is

- \dfrac{1}{\sqrt{3}}\text{,}

& then the displacement of the particle in y-direction at the instant is

Options

A $\alpha e^{- 1}$
B $\alpha e^{- 2}$
CZero
D ${\alpha}^{2} \text{e}$

Correct answer

A. $\alpha e^{- 1}$

Step-by-step solution

Here, particle is moving in two - dimensional (x – y) plane, with constant speed so slope of

graph

\dfrac{\text{d} \text{y}}{\text{d} \text{x}} = \dfrac{{v}_{y}}{{v}_{x}}

and&

{v}_{0} = \sqrt{{v}_x^{2} + {v}_y^{2}} \text{.}

As slope,

\dfrac{\text{dy}}{\text{dx}} = - \dfrac{1}{\sqrt{3}} = \dfrac{{v}_{y}}{{v}_{x}}

So,

{v}_{x} = - {v}_{y} \sqrt{3}

On squaring and adding

{v}_x^{2} + {v}_y^{2} = {v}_{0}^{2}

{3 \text{v}_y^{2} + {v}_y^{2} = {v}_{0}^{2}

{v}_{y} = \pm \dfrac{{v}_{0}}{2}

{v}_{x} = ∓ \dfrac{\sqrt{3} {v}_{0}}{2}

So,

\text{y} = \alpha e^{\dfrac{- 2}{\sqrt{3} {v}_{0}} \times \dfrac{\sqrt{3} {v}_{0}}{2}}

\text{y} = \alpha e^{- 1}

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 NTA Abhyas JEE Main PYQs