QCE Physics - Unit 3 - Gravity and motion
Projectile Motion | QCE Physics
Learn QCE Physics projectile motion with vector components, independent horizontal and vertical motion, no-drag assumptions and range data interpretation.
Updated 2026-06-15 - 5 min read
QCAA official coverage - Physics 2025 v1.3
Exact syllabus points covered
- Apply vector analysis to resolve a vector into two perpendicular components.
- Solve vector problems by resolving vectors into components, adding or subtracting the components and recombining them to determine the resultant vector.
- Describe how horizontal and vertical components of a velocity vector are independent of each other.
- Solve problems involving projectile motion in the absence of drag effects using $v_y = u_y + gt$, $s_y = u_y t + \frac{1}{2}gt^2$, $v_y^2 = u_y^2 + 2gs_y$, $v_x = u_x$ and $s_x = u_x t$.
- Interpret data relating to the horizontal distance travelled by an object projected at various angles from the horizontal.
Projectile motion is the motion of an object after it has been launched and the only significant force is gravity. The QCE version is deliberately idealised: ignore drag unless the question says otherwise, split the motion into horizontal and vertical components, then solve each direction with the right equation.
Original Sylligence diagram for physics projectile components.
Vector components
A projectile usually starts with an initial speed $u$ at an angle $\theta$ above the horizontal. That one vector needs to become two perpendicular components:
$ u_x = u\cos\theta $
$ u_y = u\sin\theta $
The horizontal component controls how far the object travels during the flight time. The vertical component controls how long the object stays in the air and how high it goes. A common QCE trap is to use the full launch speed in a vertical equation or the vertical component in a horizontal displacement equation.
Resolving and recombining vectors is not just a projectile skill. If the problem gives several vectors, resolve each into $x$ and $y$ components, add or subtract like components, then recombine:
$ R = \sqrt{R_x^2 + R_y^2} $
$ \theta = \tan^{-1}\left(\frac{R_y}{R_x}\right) $
Equations of motion
QCE projectile questions use the usual constant-acceleration equations in the vertical direction:
$ v_y = u_y + gt $
$ s_y = u_y t + \frac{1}{2}gt^2 $
$ v_y^2 = u_y^2 + 2gs_y $
In the horizontal direction, acceleration is zero in the no-drag model:
$ v_x = u_x $
$ s_x = u_x t $
The sign of $g$ depends on the sign convention. If upward is positive, use $g=-9.8\ \mathrm{m\ s^{-2}}$. If downward is positive, use $g=+9.8\ \mathrm{m\ s^{-2}}$. The calculation can be done either way, but the signs must stay consistent.
How to choose the right unknown
Most projectile questions are solved by finding time first. If the projectile starts and lands at the same height, the vertical displacement is $s_y=0$ for the whole flight. If it lands higher or lower than the launch point, use the actual vertical displacement. Once time is known, substitute it into $s_x=u_xt$ to find horizontal range.
Maximum height is different. At the top of the path, the vertical velocity is zero:
$ v_y = 0 $
That does not mean the projectile has stopped. It still has horizontal velocity. The top of the path is only the instant where the upward vertical motion has been reduced to zero before gravity accelerates the object downward.
Interpreting range data
The syllabus also expects you to interpret data relating launch angle to horizontal distance. With the same launch speed and equal launch/landing height, the ideal range is greatest at $45^\circ$. Complementary angles such as $30^\circ$ and $60^\circ$ can produce the same range in the ideal model because one has more horizontal speed and less time, while the other has less horizontal speed and more time.
Real data may not match the ideal pattern exactly. Scatter could come from air resistance, inconsistent launch speed, measurement uncertainty, spin, release height or angle-reading error. A strong data answer does three things: describes the trend, quotes data, then links the pattern to projectile physics.
Worked example
Exam-ready method
Use this order for most projectile problems:
- Draw axes and choose a sign convention.
- Resolve the initial velocity into $u_x$ and $u_y$.
- Use vertical motion to find time, height or vertical velocity.
- Use horizontal motion to find range or horizontal speed.
- Check whether the answer makes physical sense.
If the question gives a graph of range against launch angle, identify the data pattern before calculating. Physics marking often rewards interpretation of evidence, not just formula substitution.