The diagram above illustrates the path ABC, in a vertical x z plane, of a bullet shot into the air at an angle above the horizontal. Copy the diagram, and, ...

What the diagram shows. In the vertical x-z plane the bullet follows the parabolic path from A to B to C. Point A is the launch point where the bullet is rising, B is the highest point of the flight, and C is where the path returns to the horizontal on landing. The x-axis is horizontal and the z-axis is vertical.

Concept being tested. A projectile's velocity is treated as two independent parts: a horizontal component \(v_x\) and a vertical component \(v_z\). The single rule that decides how each behaves is which forces act on the bullet. Ignoring air resistance, the only force in flight is gravity, and gravity acts straight down.

• Because there is no horizontal force, there is no horizontal acceleration, so the horizontal component \(v_x\) stays constant. Its arrow has the same length and the same forward (+x) direction at A, B and C.
• Because gravity acts vertically, it produces a constant downward acceleration \(g\). This makes the vertical component \(v_z\) change continuously: it starts large and upward at A, decreases to zero at the top B, then grows downward on the way to C. By the symmetry of the parabola the upward speed at A equals the downward speed at C.

Required diagram. The path is copied below with the velocity components drawn as arrows. Notice that the three blue horizontal arrows are all the same length (constant \(v_x\)), the red vertical arrow is long and upward at A, absent at B (zero), and equally long but downward at C. The dashed purple arrow is the resultant (actual) velocity, tangent to the path.

Reading the arrows. The relative magnitudes and directions are:

So the horizontal arrows satisfy

while the vertical component follows

Common mistake to avoid. Do not shorten the horizontal arrow at the top, and do not make the bullet momentarily "stop" at B. Only the vertical component is zero at the highest point; the bullet is still moving forward at speed \(u\cos\theta\), which is why it keeps travelling and does not fall straight down. Equally, keep the horizontal arrows at A, B and C exactly the same length, because nothing pushes or drags the bullet horizontally once air resistance is ignored.

Examination reminder. Marks here are awarded for showing three equal, forward horizontal arrows and a vertical arrow that is large-up at A, zero at B, and large-down at C, with the A and C vertical arrows drawn the same length to show the up-down symmetry of projectile motion.