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JEE Main Motion in a Plane — practice questions

Explore 75 free Motion in a Plane questions in JEE Main Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Motion in a Plane: quick revision

Resolve vectors into perpendicular components before combining them. In ideal projectile motion, horizontal velocity is constant and vertical acceleration is downward. The usual range formula assumes equal launch and landing heights and negligible air resistance.

Key ideas and when to use them

  • $v=\sqrt{v_x^2+v_y^2}$.
  • $T=2u\sin\theta/g$ for return to the launch height.
  • $R=u^2\sin(2\theta)/g$ under the same assumptions.

Common mistakes

  • Add perpendicular components as vectors, not as scalar magnitudes.
  • Do not use the equal-height range formula for a launch from a cliff.

Three worked examples

Example 1: A velocity has components 3 m/s east and 4 m/s north. Find its magnitude.
  1. The components are perpendicular.
  2. $v=\sqrt{3^2+4^2}$.

5 m/s

Example 2: A projectile is launched at 20 m/s, 30° above horizontal. Find its flight time back to launch height; use g = 10 m/s².
  1. The vertical launch component is $20\sin30^\circ=10$ m/s.
  2. $T=2\times10/10$.

2 s

Example 3: Find the range at a launch speed of 20 m/s and angle 45°, returning to the same height. Use g = 10 m/s².
  1. Here $\sin(2\theta)=\sin90^\circ=1$.
  2. $R=20^2/10$.

40 m

Qallery AI-assisted study notes and original examples. Further reading: NCERT Physics — Motion in a Plane.

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Motion in a Plane questions and exercises with answers

Showing questions 1–30 of 75.

As per your syllabus, the key feature that distinguishes a vector from a scalar is which?Read the answer and worked solution →As per your syllabus, two vectors A and B are EQUAL if they have which property?Read the answer and worked solution →As per your syllabus, the sum of a vector A and its negative -A produces which result?Read the answer and worked solution →As per your syllabus, eqn 3.1, vector addition obeys which property by symmetry?Read the answer and worked solution →As per your syllabus, rain falls vertically at 35 m/s and wind blows horizontally at 12 m/s. The resultant speed is which?Read the answer and worked solution →As per your syllabus, the boy should hold his umbrella at approximately which angle to the vertical?Read the answer and worked solution →As per your syllabus, displacement (position change) is which kind of quantity?Read the answer and worked solution →As per your syllabus, examples of SCALAR quantities include which set?Read the answer and worked solution →As per your syllabus, vector subtraction A - B is defined as which operation?Read the answer and worked solution →As per your syllabus, a UNIT vector has which magnitude and which dimension?Read the answer and worked solution →As per your syllabus, eqn 3.13, the x-component of a vector A of magnitude A making angle θ with the x-axis is which?Read the answer and worked solution →As per your syllabus, eqn 3.14, the magnitude of a vector A = A_x î + A_y ĵ is which expression?Read the answer and worked solution →As per your syllabus, eqn 3.15, the angle θ that a vector A makes with the x-axis (given components A_x and A_y) is which?Read the answer and worked solution →As per your syllabus, the unit vectors along the x, y, z axes are denoted by which trio?Read the answer and worked solution →As per your syllabus, a vector in xy-plane can be written in component form as which expression?Read the answer and worked solution →As per your syllabus, vector addition by the ANALYTICAL method adds vectors by adding which?Read the answer and worked solution →As per your syllabus, the magnitude of the resultant of two vectors A and B at angle θ is given by which expression?Read the answer and worked solution →As per your syllabus, components of vector A along x and y axes are scalars whose SIGN depends on which feature?Read the answer and worked solution →As per your syllabus, if |A| = |B| = a and they make 60° between them, the magnitude of A + B is which?Read the answer and worked solution →As per your syllabus, if |A| = |B| = a and they make 90° between them, the magnitude of A + B is which?Read the answer and worked solution →As per your syllabus, eqn 3.39, the trajectory equation of a projectile y = (tan θ₀)x − [g/(2v₀²cos²θ₀)]x² describes which curve?Read the answer and worked solution →As per your syllabus, eqn 3.40a, the time t_m to reach the maximum height of a projectile is which?Read the answer and worked solution →As per your syllabus, eqn 3.40b, the time of flight T_f of a projectile (returning to launch level) is which?Read the answer and worked solution →As per your syllabus, eqn 3.41, the maximum height h_m of a projectile is which expression?Read the answer and worked solution →As per your syllabus, eqn 3.42a, the horizontal RANGE R of a projectile (same launch + landing height) is which?Read the answer and worked solution →As per your syllabus, eqn 3.42b, the projection angle θ₀ that gives MAXIMUM range (for fixed v₀) is which value?Read the answer and worked solution →As per your syllabus, launch angles (45° + α) and (45° − α) give which property of their ranges?Read the answer and worked solution →As per your syllabus, a ball thrown at 28 m/s at 30° above horizontal has maximum height of approximately which value? (g = 9.8 m/s²)Read the answer and worked solution →As per your syllabus, the time of flight for the same 28 m/s at 30° projectile is approximately which?Read the answer and worked solution →As per your syllabus, the horizontal range for the 28 m/s at 30° projectile is approximately which?Read the answer and worked solution →

Worked practice questions

As per your syllabus, the key feature that distinguishes a vector from a scalar is which?

  1. Sign
  2. Units
  3. Magnitude
  4. Direction
Show answer and solution

Correct answer: D. Direction

Your syllabus: scalar has magnitude only vector needs magnitude AND direction (and obeys triangle / parallelogram law of addition).

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As per your syllabus, two vectors A and B are EQUAL if they have which property?

  1. Same magnitude and direction
  2. Same starting point in same plane
  3. Same magnitude only (any direction)
  4. Same direction only (any magnitude)
Show answer and solution

Correct answer: A. Same magnitude and direction

Your syllabus: equality requires both magnitude and direction to match. Translation does not change a vector.

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As per your syllabus, the sum of a vector A and its negative -A produces which result?

  1. Vector identical to A
  2. Null vector (0)
  3. Vector of length 2A
  4. Vector identical to -A
Show answer and solution

Correct answer: B. Null vector (0)

syllabus eqn 3.3: A + (-A) = 0 (null vector). Magnitude zero; direction undefined.

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