Horizontal projection

G1.3 G1.4

By the end of this lesson you should be able to

Describe how horizontal and vertical components of a velocity vector are independent of each other. G1.3
Solve problems involving projectile motion in the absence of drag effects using v_y = u_y + gt, s_y = u_y t + ½gt^2, v_y^2 = u_y^2 + 2gs_y, v_x = u_x and s_x = u_x t. G1.4

Key ideas

A projectile moves under gravity alone (we ignore air resistance).
Horizontal and vertical motion are independent: gravity only changes the vertical velocity.
Horizontally: no force, so constant velocity. Vertically: constant acceleration g = 9.8 m s⁻² downwards.
For a horizontal launch, \(u_y = 0\), so a ball fired sideways and one dropped from the same height land at the same time.
Time links the two directions: find it from one direction, then use it in the other.

Key formulas (QCAA formula book notation)

\[ s_x = u_x t \]

\[ s_y = u_y t + \tfrac{1}{2} g t^2 \quad (u_y = 0) \]

\[ v_y = u_y + g t \]

Worked example

A ball rolls off a 1.25 m high table at 3.0 m s⁻¹. How far from the table does it land?

Common mistakes

Using the launch speed in the vertical equation (u_y is 0 for a horizontal launch).
Mixing sign conventions: choose up or down as positive and stick to it.
Thinking a faster horizontal speed makes the object fall more slowly.

PhET: Projectile Motion. Predict the time of flight and range first, then fire and use the measuring tool to check.

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