Quick questions on Projectile motion (QCE Physics Unit 3)

If a projectile is launched with speed $v_0$ at angle $\theta$ above the horizontal:

No horizontal force acts (air resistance is ignored), so the horizontal velocity is constant.

The only acceleration is gravity, $a_y = -g$ (taking up as positive). Use the constant-acceleration equations:

The path is a parabola. At maximum height $v_y = 0$, so the rise above the launch point is:

Expect either a launch-angle table to interpret (range vs angle data, often missing one value), or a single trajectory with annotated heights and asked to extract launch speed and landing time. Marker traps focus on candidates who plug the resultant speed in place of a component or forget to use $r = R_E + h$ on the vertical axis when a height above the launch is involved.

The standard projectile IA2 measures range as a function of launch angle for a fixed launch speed (small projectile launcher or a ball-bearing on a ramp). A strong report linearises by plotting $R$ against $\sin(2\theta)$ (slope $= v_0^2 / g$), reports a $v_0$ that agrees with a direct measurement, and discusses air-resistance and release-height systematic effects in the evaluation. The IA2 criteria reward the design justification, the data, and the evaluation in that order.

Horizontal velocity never changes (with air resistance neglected). Vertical velocity changes by $-9.8$ m/s every second. Set up two separate columns of working and never let a $\cos$ leak into a vertical equation.

If you take up as positive, $g$ enters the equations as $-9.8 \text{ m/s}^2$. If you take down as positive, $g$ is $+9.8 \text{ m/s}^2$. Pick a convention and stick to it for the whole question.

$v_0 = 25$ m/s at $40°$ does not mean the horizontal velocity is $25$ m/s. You must resolve into components first.

If a stone is thrown horizontally off a cliff, $v_{0y} = 0$. The full speed is in the horizontal direction.

$R = v_0^2 \sin(2\theta) / g$ only works when launch height equals landing height. Otherwise solve the vertical equation for $t$ first, then compute $x = v_{0x} t$.

Markers deduct for missing units (m, s, m/s) even when the number is correct.