Projectile motion — OCR A-Level Physics
Test yourself on Projectile motion with OCR A-Level practice questions.
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Projectile motion explained
A projectile is any object moving freely under gravity alone, and its motion splits into two perpendicular components that do not affect each other.
Read the full explanation
Horizontally there is no resultant force, so horizontal velocity stays constant and horizontal displacement is velocity × time. Vertically the only force is weight, giving constant downward acceleration g, so vertical velocity changes steadily and vertical displacement follows the constant-acceleration equations. Because the two directions are independent, the time of flight is fixed entirely by the vertical motion, while the horizontal range is fixed by the horizontal velocity and that same time. For example, a ball rolled off a bench and one dropped vertically from the same height reach the floor together, because both have identical vertical motion.
(b) two-dimensional motion of a projectile with constant velocity in one direction and constant acceleration in a perpendicular direction.
In two dimensions a projectile combines constant velocity in one direction with constant acceleration perpendicular to it. Taking horizontal as the constant-velocity direction and vertical as the constant-acceleration direction, the horizontal component of velocity is unchanged while the vertical component changes at a steady rate. The resultant velocity is found by vector addition of the two components, and its direction is given by the angle whose tangent is the vertical component divided by the horizontal component. Displacements are treated the same way: horizontal displacement grows linearly with time, while vertical displacement follows a constant-acceleration equation. For example, a ball thrown at an angle has initial components v cos θ horizontally and v sin θ vertically; the horizontal component stays v cos θ while the vertical component changes by g each second.
Your focus
- Describe why the horizontal and vertical motions of a projectile are independent.
- Use constant-velocity and constant-acceleration equations separately for the two perpendicular directions.
- Explain why two projectiles released from the same height with different horizontal velocities land at the same time.
Show all 6 objectives
- Resolve a projectile's initial velocity into perpendicular components.
- Apply constant-velocity and constant-acceleration equations to the correct perpendicular directions.
- Combine perpendicular velocity components to find the resultant velocity and its direction.
Projectile motion exam tips
Marking Points
- Horizontal and vertical components of a projectile's motion are independent of each other.
- Horizontally there is no resultant force, so horizontal velocity is constant and horizontal displacement = horizontal velocity × time.
- Vertically the only force is weight, giving constant downward acceleration of magnitude g, so vertical velocity changes at a steady rate.
- The time of flight is determined solely by the vertical motion; the horizontal range follows from horizontal velocity and that time.
- A projectile released horizontally and one dropped from the same height land at the same time because their vertical motions are identical.
- A projectile has constant velocity in one direction and constant acceleration in a perpendicular direction.
- The horizontal velocity component remains constant because there is no horizontal resultant force.
- The vertical velocity component changes at a constant rate because the acceleration is constant and perpendicular to the horizontal direction.
- The resultant velocity at any instant is the vector sum of the horizontal and vertical components, with direction found from the tangent of the angle between them.
- Horizontal displacement is proportional to time, while vertical displacement follows a constant-acceleration equation.
Examiner Tips
- 💡State explicitly that the two perpendicular components are independent before using any equation.
- 💡Choose the vertical direction to find time of flight, then use that time with constant horizontal velocity to find range.
- 💡Check the direction convention for g and keep signs consistent when substituting into constant-acceleration equations.
- 💡Resolve the initial velocity into perpendicular components before substituting into any equation.
- 💡Keep the two directions in separate columns of working so constant-velocity and constant-acceleration equations are not mixed up.
- 💡Find the resultant velocity by vector addition and give its direction as an angle from a stated reference direction.
Common Mistakes
- Believing that a larger horizontal velocity makes a projectile fall more slowly: the horizontal and vertical motions are independent, so the vertical fall time is unchanged.
- Treating horizontal velocity as decreasing during flight: with no horizontal resultant force it stays constant, and only the vertical velocity changes.
- Assuming the vertical acceleration changes direction or magnitude during flight: near the Earth's surface it stays constant at g downwards throughout.
- Thinking the two components must be combined before the time of flight can be found: the vertical motion alone gives the time of flight.
- Adding the horizontal and vertical speeds as ordinary numbers instead of combining them as perpendicular vectors.
- Using the constant-acceleration equations for the horizontal direction: the horizontal velocity is constant, so only displacement = velocity × time applies there.
- Forgetting to resolve an initial velocity at an angle into horizontal and vertical components before applying the equations.
- Assuming the acceleration has a component along the direction of constant velocity: the acceleration is perpendicular to it, so that component is zero.