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Projectile motion

Resolving motion into independent horizontal and vertical components under gravity.

  • Define and explain Projectile motion in your own words
  • Use key terms such as Friction accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Projectile motion: resolving motion into independent horizontal and vertical components under gravity.

Definition: Projectile motion

Resolving motion into independent horizontal and vertical components under gravity.

Key ideas

Projectile motion

Horizontal and vertical motion are independent: horizontal velocity stays constant (no air resistance), while vertical motion accelerates at g = 9.8 m/s² downwards. Resolve the initial velocity into components, then treat each direction with SUVAT.

Newton's second law

The resultant force on a particle equals mass times acceleration (F = ma). Draw a force diagram, resolve along the direction of motion, and equate; mass in kg, acceleration in m/s² gives force in newtons.

Key term — Friction: A force opposing relative motion between surfaces, modelled as F ≤ μR where μ is the coefficient of friction and R the normal reaction.

Worked example: Projectile motion

A projectile is launched horizontally at 20 m/s from a 45 m cliff. How long until it hits the sea? (g = 9.8 m/s²).

t² = 90/9.8 ≈ 9.18; t ≈ 3.03 s.

Answer: t² = 90/9.8 ≈ 9.18; t ≈ 3.03 s.

Common mistakes
  • Forgetting g = 9.8 m/s² in vertical projectile motion Vertical motion always accelerates downwards at g; a sign error here flips the whole trajectory.
  • Using F = ma with the wrong force It is the resultant (net) force that equals ma — add all forces vectorially first, including friction and weight components.

Practice

A particle starts from rest and accelerates at 3 m/s² for 5 s. Find its final velocity.
v = u + at.

v = 0 + 3 × 5 = 15 m/s.

Find the distance travelled in the previous question.
s = ut + ½at².

s = 0 + ½ × 3 × 25 = 37.5 m.

A 2 kg mass experiences a resultant force of 10 N. Find its acceleration.
F = ma.

a = 10/2 = 5 m/s².

A box on rough ground has normal reaction 50 N and μ = 0.4. Find the maximum friction.
F_max = μR.

F_max = 0.4 × 50 = 20 N.

Quick check

Projectile motion — quick check

Which of these best defines "Friction"?

A force opposing relative motion between surfaces, modelled as F ≤ μR where μ is the coefficient of friction and R the normal reaction.

A ball is dropped from rest. How far does it fall in 2 s? (g = 9.8 m/s²)

s = ½ × 9.8 × 4 = 19.6 m.
Key takeaways
  • Projectile motion: resolving motion into independent horizontal and vertical components under gravity.
  • Projectile motion: Horizontal and vertical motion are independent: horizontal velocity stays constant (no air resistance), while vertical motion accelerates at g = 9.8 m/s² downwards.
  • Displacement: Distance measured in a straight line from a starting point, with direction included; unlike distance, it can be negative.
  • Watch out for: forgetting g = 9.8 m/s² in vertical projectile motion
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