Motion in a Plane JEE Main PYQs (2020–2026)

Solved Motion in a Plane PYQs

3 recent questions with answers. The full set of 71 is free to practise.

1. JEE Main 2025MediumProjectile Motion
   Q1

   Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. $T_1$ and $T_2$ are the total flying times of first and second ball, respectively, then the ratio of $T_1$ and $T_2$ is

   • A2 : 1
   • B$\sqrt{2}:1$
   • C2 $\sqrt{2}:1$
   • D4 : 1

   Show answer & solution

   Correct answer: (C)

   Given that the maximum height reached by the first ball is 8 times that of the second ball:
   
   $${\left(H_{\max }\right)}_1=8\times {\left(H_{\max }\right)}_2$$
   
   We can relate this to the initial velocities and angles using the formula for maximum height:
   
   $$\frac{u^2{\sin }^2{\theta }_1}{2g}=8\times \frac{u^2{\sin }^2{\theta }_2}{2g}$$
   
   Simplifying, we find:
   
   $$\sin {\theta }_1=2\sqrt{2}\sin {\theta }_2$$
   
   Now, the ratio of the total flying times $T_1$ and $T_2$ is given by:
   
   $$\frac{T_1}{T_2}=\frac{2u\sin {\theta }_1/g}{2u\sin {\theta }_2/g}=\frac{\sin {\theta }_1}{\sin {\theta }_2}=2\sqrt{2}$$
   
   Thus, the ratio of $T_1$ to $T_2$ is $2\sqrt{2}:1$ .
2. JEE Main 2024EasyPosition, Velocity and Acceleration in Two Dimensions
   Q2

   Position of an ant ( $S$ in metres) moving in $Y$ - $Z$ plane is given by $S=2t^2\hat{j}+5\hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t=1s$ will be :

   • A$16m/s$ in $y$ -direction
   • B$4m/s$ in $x$ -direction
   • C$9m/s$ in $z$ -direction
   • D$4m/s$ in $y$ -direction

   Show answer & solution

   Correct answer: (D)

   The position of an ant, denoted as $S$ in meters, moving in the $Y$ - $Z$ plane is given by $=2t^2\hat{j}+5\hat{k}$ , where $t$ is in seconds. To determine the magnitude and direction of the ant’s velocity at $t=1$ second, we need to differentiate the position function with respect to time.
   
   The velocity $\overrightarrow{v}$ is given by:
   
   $$\overrightarrow{v}=\frac{dS}{dt}=\frac{d}{dt}(2t^2\hat{j}+5\hat{k})$$
   
   On differentiating, we get:
   
   $$\overrightarrow{v}=4t\hat{j}$$
   
   At $t=1$ second:
   
   $$\overrightarrow{v}=4\cdot 1\hat{j}=4\hat{j}$$
   
   Therefore, the magnitude of the velocity is $4m/s$ and it is directed along the $y$ -axis.
3. JEE Main 2020MediumUniform Circular Motion
   Q3

   A particle moves such that its position$\overrightarrow{r}(t)=cos\omega t\hat{i}+sin\omega t\hat{j}$ where $\omega$ is a constant and t is time. Then which of the following statements is true for the velocity $\overrightarrow{v}(t)$ and acceleration $\overrightarrow{a}(t)$ of the particle :

   • A$\overrightarrow{v}$ and $\overrightarrow{a}$ both are perpendicular to $\overrightarrow{r}$
   • B$\overrightarrow{v}$ and $\overrightarrow{a}$ both are parallel to $\overrightarrow{r}$
   • C$\overrightarrow{v}$ is perpendicular to $\overrightarrow{r}$ and $\overrightarrow{a}$ is directedthe origin
   • D$\overrightarrow{v}$ is perpendicular to $\overrightarrow{r}$ and $\overrightarrow{a}$ is directedfrom the origin

   Show answer & solution

   Correct answer: (C)

   $$\overrightarrow{r}(t)=cos\omega t\hat{i}+sin\omega t\hat{j}$$
   
   $\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}$ = $-\omega \sin \omega t\hat{i}+\omega \cos \omega t\hat{j}$
   
   $\overrightarrow{a}=\frac{d\overrightarrow{v}}{dt}$ = $-{\omega }^2\cos \omega t\hat{i}-{\omega }^2\sin \omega t\hat{j}$
   
   = $-{\omega }^2\left(\cos \omega t\hat{i}+sin\omega t\hat{j}\right)$
   
   = $-{\omega }^2\overrightarrow{r}$
   
   $$\therefore \overrightarrow{a}$$
   
   is antiparallel to $\overrightarrow{r}$ and it’s direction towards the origin.
   
   $\overrightarrow{v}.\overrightarrow{r}=\omega \left(-sin\omega t\cos \omega t+cos\omega t\sin \omega t\right)$ = 0
   
   So $\overrightarrow{v}\perp \overrightarrow{r}$ .

Topic-wise question count

Where JEE Main has asked from Motion in a Plane, most frequent first.

• Projectile Motion51
• Position, Velocity and Acceleration in Two Dimensions10
• Relative Velocity in Two Dimensions9
• Uniform Circular Motion1

Year-wise Motion in a Plane questions in JEE Main

Number of questions from this chapter in each year's paper(s).