Topic 6 - 2D Kinematics and Projectile Motion

Question 1

How do we move Kinematics Equations to 2D?

Answer 1

To turn questions into 2D, we simply look at the x- and y- components separately!
* This means we have to decompose displacement, velocity, acceleration vectors into x and y components
* And then apply kinematics equations to just x and then just y components to find final values

Question 2

Displacement (Δ ⃑𝑟)

Answer 2

The change in position of an object in motion

Question 3

Average Velocity ( ⃑v)

Answer 3

The displacement divided by time passed

Question 4

Average Acceleration ( ⃑𝑎)

Answer 4

The change in velocity over a period of time

Question 5

Projectile Motion

*assume the following

Answer 5

Question 6

Analyzing Projectile Motion

Answer 6

When analyzing projectile motion, the horizontal and vertical motions are completely independent of each other – don’t mix them up

Question 7

x-component of velocity (𝑣𝑥)

Answer 7

Does not change with time

• But, gravitational acceleration still affects
  vertical motion!

Question 8

Summary of Projedctile Motion

Answer 8

1. Provided air resistance is negligible, the horizontal component of velocity 𝑣𝑥 remains constant as there is no horizontal component of acceleration
2. The vertical component of acceleration is equal to the free-fall acceleration−𝑔
3. The vertical component of the velocity 𝑣𝑦 and the displacement in the 𝑦-direction are
   identical to those of a freely falling body
4. Projectile motion can be described as a superposition of two independent motions in the 𝑥− and 𝑦− directions.

Question 9

2D Motion: General Case

What happens if we do include air resistance or engines in the x-direction?

Answer 9

• We first have to guarantee that acceleration is constant and not changing (otherwise our kinematics equations won’t work)
• Do the exact same thing as projectile motion, but apply kinematics equations to both the x- and y-directions.

Question 10

Problem Solving Approach to 2D Motion

Answer 10

1. Read the question and highlight was your end goal is (what you’re trying to find)
2. Pick a coordinate system (+x, +y) and draw a diagram with the path of motion. Label
   everything and list all known/unknown variables.
3. Decompose all values into x- and y-components and treat them separately
   * It may help to split the page into two (x-analysis on the left; y-analysis on the right)
   * Do not get the two mixed up
4. Apply kinematics equations (constant acceleration) or 𝑣𝑥 = 𝑟𝑥/𝑡 (zero acceleration) to analyze the horizontal and vertical motion of the object independently
5. Use your x- and y-component final values to determine the resultant vector as needed.

Question 11

Key Equations and Concepts

Answer 11

Key things to remember:
* Treat the x- and y-directions completely separately, then combine them in the end
* If 𝑎𝑥 ≠ 0, use the kinematics equations as you’re now looking at general 2D motion