Topic 5: Projectile Motion

Projectile Motion

Projectile motion is the motion of a body projected into air with some initial velocity and then allowed to move under the action of gravity alone.

In projectile motion, air resistance is neglected and acceleration due to gravity acts vertically downward.

Examples of Projectile Motion

  • A ball thrown at an angle to the horizontal
  • A stone thrown from the top of a building
  • A bullet fired from a gun

Components of Projectile Motion

The motion of a projectile can be resolved into two independent motions:

  • Horizontal motion (along x-axis)
  • Vertical motion (along y-axis)

Initial Velocity Components

If a projectile is thrown with initial velocity u at an angle θ with the horizontal, then:

Horizontal component: ux = u cosθ
Vertical component: uy = u sinθ

Important Characteristics

  • Horizontal velocity remains constant
  • Vertical velocity changes due to gravity
  • Path followed by projectile is a parabola

Important Formulae of Projectile Motion

  • Time of flight: T = (2u sinθ) / g
  • Maximum height: H = (u² sin²θ) / (2g)
  • Horizontal range: R = (u² sin2θ) / g

Special Case: Maximum Range

The horizontal range of a projectile is maximum when θ = 45°.

Q1. Projectile motion is a type of:
A) One-dimensional motion
B) Circular motion
C) Two-dimensional motion
D) Oscillatory motion

Answer: C


Q2. In projectile motion, the horizontal velocity:
A) Increases
B) Decreases
C) Remains constant
D) Becomes zero

Answer: C


Q3. The path followed by a projectile is:
A) Straight line
B) Circular
C) Elliptical
D) Parabolic

Answer: D


Q4. Which force acts on a projectile during its motion?
A) Magnetic force
B) Electric force
C) Frictional force
D) Gravitational force

Answer: D


Q5. Time of flight of a projectile depends on:
A) Horizontal velocity
B) Vertical component of velocity
C) Mass of projectile
D) Shape of projectile

Answer: B


Q6. Maximum range is obtained when angle of projection is:
A) 30°
B) 45°
C) 60°
D) 90°

Answer: B


Q7. Formula for horizontal range is:
A) u² sinθ / g
B) u² cosθ / g
C) u² sin2θ / g
D) 2u sinθ / g

Answer: C


Q8. At the highest point of projectile motion, the vertical velocity is:
A) Maximum
B) Minimum
C) Zero
D) Equal to u

Answer: C

Chapter 4: Motion in a Plane

Topic 5: Projectile Motion – Quick Revision

1. Definition

Projectile motion is the motion of a body projected into air and moving under gravity alone.

2. Velocity Components

ux = u cosθ
uy = u sinθ

3. Important Formulae

  • Time of flight: T = (2u sinθ) / g
  • Maximum height: H = (u² sin²θ) / (2g)
  • Range: R = (u² sin2θ) / g

4. Key Points

  • Horizontal motion is uniform
  • Vertical motion is uniformly accelerated
  • Path is parabolic
  • Maximum range at 45°

Exam Focus (MHT-CET)

MCQs and numericals are frequently asked on formulae, angle conditions and special cases.


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