Q: Kinematics: Model motion under gravity in a vertical plane using vectors; projectiles.

The idea

This topic models projectile motion in a vertical plane using vectors. Assuming no air resistance, acceleration is constant: a = -gj (taking j as vertical). Velocity and displacement are found by integrating: v = u + at and r = ut + ½at², where u is initial velocity. Resolve initial velocity into horizontal and vertical components. The horizontal component remains constant; the vertical component changes due to gravity. Solve problems such as finding time of flight, maximum height, range, or speed at a given time.

For example: A ball projected at 20 m/s at 30° to the horizontal: u = 20cos30°i + 20sin30°j, then use equations to find position at any time.

What earns the marks

• Resolve initial velocity into horizontal and vertical components using trigonometry.
• Apply constant acceleration equations separately to horizontal and vertical motion.
• Use vector equations v = u + at and r = ut + ½at² to find velocity and position at a given time.
• Determine key features such as time of flight, maximum height, range, and speed on impact.
• Interpret the model, including assumptions such as negligible air resistance and acceleration due to gravity.

Common mistakes and how to put them right

• Using the same acceleration for horizontal and vertical motion.

  Put it right: Horizontal acceleration is zero, vertical acceleration is -g.

• Forgetting to resolve initial velocity into components.

  Put it right: Start by finding u_x and u_y.

• Mixing up displacement and distance.

  Put it right: Displacement is a vector, distance is scalar.

Exam tips

• Draw a clear diagram showing the initial velocity, angle, and coordinate axes.
• State the equations you use and substitute values carefully, keeping components separate.
• Check whether the question asks for a vector or scalar quantity, and give units where appropriate.