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Week 3 — Motion in 2D and Relative Motion in 2D. Pick a mode. Start a timer. That's it.

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The shortest path to walking in prepared.

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5-minute version

Three skills. One sentence each.

2D kinematics — apply each SUVAT equation per plane; only $t$ links $x$ and $y$ .
Projectile motion — set $a_{x} = 0$ , $a_{y} = \pm g$ (sign depends on whether $+ y$ is up or down); horizontal velocity never changes.
Relative velocity — $v_{O G} = v_{O M} + v_{M G}$ , component-wise.

Open the cheatsheet quiz, do 3 easy questions, close it. You’re prepped.

Reminder. Portfolio 2 is assessed in this week’s Workshop class (slide 21). Bring Week 2 eContent, Lecture 3 notes, and Tutorial 3 worked.

Time	Action
0–5 min	Skim the cheatsheet tables — especially the per-plane SUVAT table and the relative-velocity subscript convention.
5–10 min	Work one problem of each type with pen and paper: a projectile (Exercise 2), a relative-velocity (Exercise 4).
10–15 min	Take the cheatsheet quiz. Don’t worry about the score — review the explanations on anything you miss.
15–20 min	Read the matching “common mistakes” + the exam-style worked example in the in-depth note.

Most students slip on three specific things in this week:

The sign of $g$ . Choose $+ y$ up or $+ y$ down once, then be consistent throughout the problem. If $+ y$ is up, $a_{y} = - 9.81$ ; if $+ y$ is down, $a_{y} = + 9.81$ .
The $tan^{- 1}$ quadrant correction. Calculator returns angles in $(- 90°, 90°)$ only. For quadrants 2 and 3, add $180°$ .
Differentiating between planes. $x$ and $y$ SUVAT equations are independent. Only $t$ is shared. Do not substitute $u_{y}$ into an $x$ -equation.

The four SUVAT equations, valid per plane when $a$ is constant:

v = u + a t, v^{2} = u^{2} + 2 a s, s = u t + \frac{1}{2} a t^{2}, s = \frac{u + v}{2} t

Polar ↔ Cartesian:

A_{x} = A cos θ, A_{y} = A sin θ, A = A_{x}^{2} + A_{y}^{2}, θ = tan^{- 1} (A_{y} / A_{x}) (+ 180° in Q2/Q3)

Projectile (no air resistance):

a_{x} = 0, a_{y} = \pm g

Relative velocity:

v_{O G} = v_{O M} + v_{M G} (applied per plane)

Task type	What the setup usually looks like
Velocity-time graph reading	Find displacement as the area under each component graph
Horizontal-launch projectile	Object leaves a surface at $u_{x}$ , drops $h$ ; find horizontal range
Angled-launch projectile	Given $∥ u ∥$ and $θ$ ; find time of flight, range, or max height
Relative motion	Plane/boat/swimmer in a moving medium; find one of the three velocities

Portfolio 2 (the assessment for this Workshop) draws from these patterns.

Forgetting to convert km/h to m/s (divide by $3.6$ ) before mixing with $g = 9.81$ m/s $^{2}$ .
Treating ” $v_{y} = 0$ at the peak” as also meaning ” $v_{x} = 0$ .” It doesn’t — only the vertical component is zero.
Using SUVAT when acceleration isn’t constant (e.g. drag problems).
Adding velocities as if they were scalars — relative velocity is vector addition, component-wise.
Skipping the sketch. The “Visualise” step (slide 7) catches most direction errors.
Quoting an answer with no units or wrong sign — auto-mark loses 30% there.

Try these without notes. Five minutes total.

A ball is kicked horizontally off a $20$ m cliff at $15$ m/s. How long until it hits the ground, and how far from the base of the cliff does it land? Use $g = 9.8$ m/s $^{2}$ .
A projectile is launched from ground level at $40$ m/s at $30°$ above the horizontal. Find its maximum height above launch. Use $g = 9.8$ m/s $^{2}$ .
A swimmer crosses a river. She swims at $1.2$ m/s due north relative to the water. The current flows east at $0.5$ m/s relative to the ground. What is her speed and direction relative to the ground?

Answers:

Question	Answer
1	$t = 2 (20) /9.8 \approx 2.02$ s; horizontal distance $= 15 \times 2.02 \approx 30.3$ m
2	$u_{y} = 40 sin 30° = 20$ m/s; $h_{max} = u_{y}^{2} / (2 g) = 400/19.6 \approx 20.4$ m
3	$v_{O G} = 0.5 \hat{i} + 1.2 \hat{j}$ m/s; $∥ v_{O G} ∥ = 0.25 + 1.44 = 1.3$ m/s; $θ = tan^{- 1} (0.5/1.2) \approx 22.6°$ east of north

That’s it. Close the laptop.