HSC Physics — Module 1
Vectors — Flashcards & Quiz
Vectors are quantities with both magnitude and direction, and fluent vector manipulation is the foundation of HSC Physics Module 1. You need to distinguish scalar (mass, time, distance) from vector (displacement, velocity, force) quantities, add vectors by the head-to-tail and parallelogram methods, resolve a vector into perpendicular components using sinθ and cosθ, and calculate the resultant magnitude using Pythagoras.
Key Points
- Scalars have magnitude only (mass, time, energy, speed); vectors have magnitude AND direction (displacement, velocity, acceleration, force).
- Vector addition: use head-to-tail (draw the second vector starting from the first's head) or parallelogram (common origin, complete the parallelogram).
- A vector can be resolved into perpendicular components: horizontal = V cos θ, vertical = V sin θ, where θ is measured from the horizontal.
- Resultant magnitude from perpendicular components: R = √(x² + y²); direction: θ = tan⁻¹(y/x).
- Relative velocity: if A moves at v_A and B moves at v_B, the velocity of A relative to B is v_A − v_B (vector subtraction).
- Exam trap: never add speeds directly when they are in different directions — always decompose into components and add component-wise.
Common Mistakes to Avoid
- Adding vectors as scalars — you must account for direction.
- Forgetting the difference between distance (scalar, total path) and displacement (vector, straight-line).
- Using sin for horizontal and cos for vertical — it's the opposite for angles measured from horizontal.
- Neglecting to check the quadrant when calculating angles — θ = tan⁻¹(y/x) can be ambiguous.
- Treating velocity and speed as the same thing — velocity is a vector, speed is its magnitude.
Exam Strategy
HSC Module 1 vector questions ask you to (1) add or subtract vectors, (2) resolve into components, or (3) find relative velocity. Method: draw a diagram, decompose each vector into perpendicular components (x and y), add components separately, recombine using Pythagoras and arctan. Always label direction clearly.
Sample Flashcards
Q1: What is the difference between a scalar and a vector quantity?
A scalar has magnitude only (e.g. speed, distance, mass, energy, time). A vector has both magnitude and direction (e.g. velocity, displacement, acceleration, force). Vectors are represented by arrows whose length indicates magnitude and orientation indicates direction.
Q2: How do you add two vectors that are not in the same direction?
Use the head-to-tail method: draw the first vector, place the tail of the second at the head of the first. The resultant is from the tail of the first to the head of the last. For perpendicular vectors, use Pythagoras. For others, use the sine and cosine rules or resolve into components.
Q3: How do you resolve a vector into perpendicular components?
For a vector V at angle θ to the horizontal: horizontal component V_x = Vcosθ; vertical component V_y = Vsinθ. This allows 2D problems to be solved as two independent 1D problems.
Sample Quiz Questions
Q1: Speed is a vector quantity because it describes how fast an object is moving.
Answer: FALSE
Speed is a SCALAR — it has magnitude only (how fast). Velocity is the vector equivalent, having both magnitude and direction. Speed = |velocity|.
Q2: Two vectors of magnitude 3 N and 4 N always produce a resultant of 7 N.
Answer: FALSE
The resultant depends on the angle between them. Maximum = 3 + 4 = 7 N (same direction). Minimum = 4 - 3 = 1 N (opposite direction). At 90°: √(9+16) = 5 N. The resultant ranges from 1 N to 7 N.
Q3: When resolving a vector into components, the component is always smaller than the original vector.
Answer: TRUE
Each component = V×cosθ or V×sinθ, and since cos and sin are ≤ 1 (for 0° < θ < 90°), each component is smaller than the original vector. The original vector is the hypotenuse of the right triangle formed by its components.
Revision Tip
Vector addition is geometric — drill Revizi flashcards that give you two vectors and ask for their resultant (both magnitude and direction).
Related Concepts
Last updated: March 2026 · 3 flashcards · 3 quiz questions