Kinematics Part 2 (AS-Level)

What these notes cover

These notes cover projectile motion for Cambridge International AS Level Physics (9702): resolving the initial velocity into horizontal and vertical components, applying the equations of motion separately in each direction, the time to maximum height, total time of flight, maximum height and range, objects projected horizontally from a height (half-projectile motion), the resultant velocity at any instant, and the effect of air resistance on the path. They include worked examples and past-paper questions.

Key formulas and definitions

• A projectile moves in two dimensions. With air resistance negligible, the horizontal and vertical motions are independent and can be treated separately.
• Horizontal: velocity is constant, u_x = u cos θ, so the horizontal distance is x = (u cos θ) t.
• Vertical: constant acceleration g = 9.81 m s⁻² downwards, with initial vertical velocity u_y = u sin θ. Use v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t.
• At the maximum height the vertical component of velocity is zero, but the horizontal component is not. Time to maximum height = u sin θ / g, and total time of flight on level ground = 2u sin θ / g.
• Maximum height: H = (u sin θ)² / 2g.
• Resultant velocity at any instant: v = √(v_x² + v_y²), at an angle α to the horizontal where tan α = v_y / v_x.
• For an object projected horizontally from a height h, the initial vertical velocity is zero: time to fall t = √(2h / g), and horizontal distance = ut.
• The acceleration (and the resultant force, the weight) acts vertically downwards at every point of the path. With air resistance, the maximum height and range are smaller and the path is no longer symmetrical.