Why does a horizontally launched object follow a curved path, and how do we treat its motion?
Projectile motion: treating a projectile as separate horizontal (constant velocity) and vertical (constant acceleration) motions, and using these to find the range, time of flight and impact velocity.
An SQA National 5 Physics answer on projectile motion, covering why a projectile is treated as separate horizontal and vertical motions, that the horizontal velocity is constant while the vertical motion accelerates under gravity, and how to find the range, time of flight and impact speed of a horizontally launched projectile.
Reviewed by: AI editorial process; not yet individually human-reviewed
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What this key area is asking
The SQA wants you to treat a projectile as two separate motions, a constant-velocity horizontal motion and a constant-acceleration vertical motion, and to use these to find the range, the time of flight and the impact velocity of a horizontally launched object.
Why split the motion?
This is why a ball thrown horizontally and a ball simply dropped from the same height land at the same instant: their vertical motions are identical, and the sideways motion of the thrown ball makes no difference to how fast it falls.
The horizontal motion
Horizontally there is no force (air resistance is ignored), so by Newton's first law the horizontal velocity is constant. The horizontal distance, called the range, is found with the constant-speed relationship:
The vertical motion
Vertically the projectile accelerates downwards at . For a horizontally launched projectile the initial vertical velocity is zero, so the vertical velocity grows from zero:
You can also read the vertical motion from a velocity-time graph: a horizontal line for the constant horizontal velocity, and a straight upward slope from zero for the vertical velocity.
Satellites: a projectile that never lands
The SQA links projectiles to satellites. A satellite is a projectile moving so fast horizontally that, as it falls towards the Earth, the curved surface of the Earth falls away beneath it at the same rate. It is in constant free fall but never gets closer to the ground, so it stays in orbit. This idea is developed further in the Space area.
Try this
Q1. State what is true about the horizontal velocity of a projectile (ignoring air resistance). [1 mark]
- Cue. It stays constant, because no horizontal force acts.
Q2. A ball is thrown horizontally at and is in the air for . Calculate the horizontal range. [2 marks]
- Cue. .
Q3. For the same ball, calculate the vertical speed just before landing (). [2 marks]
- Cue. .
Exam-style practice questions
Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
SQA N5 style4 marksA ball is thrown horizontally from a cliff at 5.0 m s per second and lands 2.0 s later. Calculate the horizontal distance travelled and the vertical speed just before it lands (g = 9.8 m s per second per second).Show worked answer →
Treat the two directions separately.
Horizontal: the velocity is constant, so distance .
Vertical: the ball starts with zero vertical velocity and accelerates at , so .
Markers reward using the constant horizontal velocity for the range, the constant vertical acceleration for the vertical speed, and the correct units.
SQA N5 style3 marksExplain why a ball thrown horizontally and a ball dropped from rest at the same height hit the ground at the same time.Show worked answer →
The horizontal and vertical motions are independent. The horizontal velocity has no effect on the vertical motion.
Both balls start with zero vertical velocity and fall under the same vertical acceleration from the same height, so their vertical motions are identical.
Because the time to fall depends only on the vertical motion, both balls take the same time to reach the ground. The thrown ball simply also travels sideways while it falls.
Markers reward stating that the two motions are independent and that the vertical motion is the same for both.
Related dot points
- Vectors and scalars: distinguishing the two kinds of quantity, the difference between distance and displacement and between speed and velocity, and combining vectors that act at right angles.
An SQA National 5 Physics answer on vectors and scalars, covering which quantities are scalar and which are vector, the difference between distance and displacement and between speed and velocity, and how to combine two vectors that act at right angles using a scale diagram or Pythagoras.
- Velocity and acceleration: defining and calculating acceleration, and interpreting velocity-time graphs to describe motion and to find acceleration and distance travelled.
An SQA National 5 Physics answer on velocity and acceleration, covering the definition and calculation of acceleration, how it is measured with light gates, and how to read a velocity-time graph to describe the motion, find the acceleration from the gradient and find the distance from the area under the line.
- Newton's laws: balanced and unbalanced forces, Newton's first and second laws including F equals ma, the difference between mass and weight, and friction and free-body force diagrams.
An SQA National 5 Physics answer on Newton's laws, covering balanced and unbalanced forces, Newton's first and second laws including F equals ma, the difference between mass and weight using W equals mg, terminal velocity, and how to find a resultant force from a free-body diagram.
- Energy: work done by a force, gravitational potential energy and kinetic energy, the conservation of energy, and using energy changes to solve motion problems such as a falling or braking object.
An SQA National 5 Physics answer on energy in dynamics, covering work done by a force, gravitational potential energy and kinetic energy, the conservation of energy, and how to combine these to solve problems such as a falling object or a braking car.
Sources & how we know this
- SQA National 5 Physics Course Specification — SQA (2019)