OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(b) two-dimensional motion of a projectile with constant velocity in one…
Full specification wording
Projectile 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.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 2 of 2
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
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.
What earns the marks
- 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.
Common mistakes and how to put them right
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.
Put it right: 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.
Put it right: The acceleration is perpendicular to it, so that component is zero.
Exam tips
- 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.
Try the lesson
The start of the Projectile motion: (b) two-dimensional motion of a projectile with constant velocity in one direction and constant acceleration in a perpendicular direction. lesson, made from checked teaching notes for this specification point.
Listen
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. A strong answer earns marks for these points. 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. Exam tip: Resolve the initial velocity into perpendicular components before substituting into any equation.
See it
Key words
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Vector resolution of velocity
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Constant velocity in one direction
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Constant acceleration perpendicular to that direction
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Vector addition of perpendicular components
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See every definition
- Vector resolution of velocity
- Splitting an initial velocity at an angle into perpendicular components, such as v cos θ horizontally and v sin θ vertically.
- Constant velocity in one direction
- The horizontal component of velocity is unchanged because there is no horizontal resultant force.
- Constant acceleration perpendicular to that direction
- The vertical velocity component changes at a steady rate because the acceleration is constant and perpendicular to the horizontal direction.
- Vector addition of perpendicular components
- 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.
Label the diagram
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1Box 1
2Box 2
3Box 3
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