AshPhys

Projectile motion

AshPhys · Revision cheat sheet
AS Level9702 AS Ch.2Chapter 2: Accelerated motionLesson 2.13Sections 2.13

Goal: Treat horizontal and vertical motion separately for an object launched horizontally.

velocity

01The big picture

With no air resistance, a projectile’s horizontal and vertical motions are independent. Horizontally there is no force, so the velocity stays constant. Vertically it accelerates at gg downwards, exactly like a dropped object.

The time in the air is the link: find it from the vertical motion, then use it for the horizontal distance. The path is a parabola.

Projectile [paraphrase]
An object moving under gravity alone after it is launched.
Fig. 1 · Thrown horizontally from a cliff
Thrown horizontally from a cliffA stone leaves the top of a cliff horizontally and follows a parabola to the ground. At the start, after 1 s and after 2 s, a horizontal velocity arrow of the same length is drawn; a downward vertical velocity arrow grows longer with time.uxuxuxvyvycliff
The horizontal arrows stay the same length; the vertical arrows grow by gg every second.

02Key equations

Horizontal (constant)
x=uxtx = u_x t
Vertical (from rest)
y=12gt2y = \tfrac{1}{2}gt^{2}
Vertical velocity
vy=gtv_y = gt
Symbols and units
  • x, yx,\ yhorizontal, vertical distancem\mathrm{m}
  • uxu_xhorizontal velocitym s−1\mathrm{m\,s^{-1}}
  • vyv_yvertical velocitym s−1\mathrm{m\,s^{-1}}

03Sample problems with solutions

Sample 1 · Rolling off a table
A ball rolls off a table 1.8 m high at 3.0 m s⁻¹. Calculate how far from the table it lands.

  1. Vertical: falls 1.8 m from rest:

    t=2yg=2×1.89.81=0.606 st = \sqrt{\frac{2y}{g}} = \sqrt{\frac{2 \times 1.8}{9.81}} = 0.606\ \mathrm{s}

  2. Horizontal: constant 3.0 m s⁻¹:

    x=uxt=3.0×0.606=1.82 mx = u_x t = 3.0 \times 0.606 = 1.82\ \mathrm{m}
Answer: x=1.8 mx = 1.8\ \mathrm{m} from the table
Unit check: m s−1×s=m ✓\mathrm{m\,s^{-1}} \times \mathrm{s} = \mathrm{m}\ \checkmark

04Practice problems

  1. P1
    A ball is dropped as an identical ball is thrown horizontally from the same height. Which lands first?
    Final answerThey land together
    Answer: They land together
  2. P2
    A stone is thrown horizontally at 15 m s⁻¹ from a 45 m cliff (Fig. 1). How long is it in the air?
    Final answer3.0 s (3.03 s)
    Answer: 3.0 s (3.03 s)
  3. P3
    How far from the cliff does it land?
    Final answer45 m (45.4 m)
    Answer: 45 m (45.4 m)
  4. P4
    Find its vertical velocity just before it lands.
    Final answer30 m s⁻¹ (29.7 m s⁻¹) downwards
    Answer: 30 m s⁻¹ (29.7 m s⁻¹) downwards

05Other useful information

Common mistakes

  • ✗ Wrong: Let the horizontal velocity change during the flight.

    ✓ Right: With no air resistance it stays uxu_x; only vyv_y grows.

Exam tips

  • Make two columns, horizontal and vertical; only tt crosses between them.

What the syllabus asks

  • 9702 topic 2: uniform velocity plus a perpendicular uniform acceleration. Coursebook 2.13.

Explore: Practice questions for this lesson