Projectile Motion
- A projectile is a particle moving freely, under gravity, in a two-dimensional plane
- Examples of projectile motion include:
- Sports such as basketball, javelin, archery, etc
- Computer games such as Angry Birds
What is a projectile?
Projectile Motion
- The trajectory of an object undergoing projectile motion consists of a vertical component and a horizontal component
- These need to be evaluated separately
- The key parts of the motion are:
- The acceleration due to gravity is g and is constant and downwards throughout the motion
- The horizontal velocity, vH is constant and in the direction of the object throughout the motion
- The vertical velocity, vV changes in magnitude and direction throughout the motion e.g. at the top, vV = 0
Velocity & acceleration of a projectile
Acceleration and horizontal velocity are always constant whilst vertical velocity changes
- Some key terms to know and calculate are:
- Time of flight: how long the projectile is in the air
- Maximum height attained: the height at which the projectile is momentarily at rest
- Range: the horizontal distance travelled by the projectile
- Some key terms to know, and how to calculate them, are:
How to find the time of flight, maximum height and range
Problems involving projectile motion
- There are two main considerations for solving problems involving two-dimensional motion of a projectile are:
- Constant velocity in the horizontal direction
- Constant acceleration in the vertical direction towards the Earth (due to gravity)
- The only force acting on the projectile, after it has been released, is the gravitational pull of the Earth on the object, or its weight
- Projectiles are often launched from an angle but are not necessarily always from the ground
Worked example
A motorcycle stunt-rider moving horizontally takes off from a point 1.25 m above the ground, landing 10 m away as shown.
What was the speed at take-off? (ignoring air resistance)
Worked example
A ball is thrown from a point P with an initial velocity u of 12 m s-1 at 50° to the horizontal.
What is the value of the maximum height at Q? (ignoring air resistance)
Exam Tip
Make sure you don’t make these common mistakes:
- Mixing up positive and negative values for vectors
- Mixing up velocities and distances between horizontal and vertical motion
- Confusing the direction of sin θ and cos θ
- Not converting units (mm, cm, km etc.) to metres
Further, it is worth noting that projectile motion is typically symmetrical when air resistance is ignored allowing for use of the peak to find the time of total flight or total horizontal distance by doubling the amount to get from the start point to the peak.
In these exam questions, unless specified, fluid resistance can be ignored
