01 Key Concepts
Independence of Perpendicular Motion
Motion in the x-direction and y-direction can be analyzed completely separately, since forces or velocity in one direction don't affect the other.
Position Vector
The position of an object in 2D can be written as (x,y), specifying its location along two perpendicular axes.
Velocity Components
A velocity vector can be split into horizontal (vx) and vertical (vy) components, often using vx=v*cos(theta) and vy=v*sin(theta) for a velocity v at angle theta.
Relative Velocity
The velocity of one object as observed from another moving object, found by vector subtraction: v_relative = v_A - v_B.
Resultant Vector
The single combined vector representing the net effect of two or more vectors added together.
02 Key Formulas
- vx = v*cos(theta)
- vy = v*sin(theta)
- Resultant magnitude = sqrt(vx^2+vy^2)
03 Solved Examples
Example 1 A velocity has magnitude 10 m/s at angle 30° above horizontal. Find its horizontal component (vx). (cos(30°)~0.866)
- Apply vx = v*cos(theta) = 10*cos(30°).
- = 10*0.866.
Answer: vx ≈ 8.66 m/s
Example 2 Using the same velocity, find its vertical component (vy). (sin(30°)=0.5)
- Apply vy = v*sin(theta) = 10*sin(30°).
- = 10*0.5.
Answer: vy = 5 m/s
Example 3 A boat moves at 5 m/s east relative to water, and the water flows at 2 m/s east relative to the ground. Find the boat's velocity relative to the ground.
- Add the velocities since they're in the same direction: 5 + 2.
Answer: 7 m/s east
04 Practice Questions
1A velocity has magnitude 20 m/s at 0° (purely horizontal). Find vx and vy.
vx=20, vy=0
2A velocity has magnitude 10 m/s at 90° (purely vertical). Find vx and vy.
vx=0, vy=10
3What does 'independence of perpendicular motion' mean?
Horizontal and vertical motion can be analyzed completely separately
4Find the resultant magnitude of vx=3, vy=4.
5
5A swimmer swims at 3 m/s across a river while the current pushes at 4 m/s downstream. Find the resultant speed.
5 m/s (using sqrt(3^2+4^2))
📄 Motion in Two Dimensions — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.