2-Dimensional

MotionVECTOR COMPONENTS AND ADDITION

PROJECTILES – HORIZONTAL AND ANGLED

Vectors – magnitude and direction

Drawn to scale

5m 15 m

Vector Addition: Vectors are drawn tip-to-tail

Expressed as 𝐴+ 𝐵

Where one vector ends, begin the next vector

The order doesn’t matter, but the size and direction does

The Resultant is the vector sum: draw it from beginning to end

R = 20 m

Vector Addition and Subtraction

Vector Subtraction

Expressed as 𝐴− 𝐵

Just means to change the direction of vector B by 180 degrees

R = 5-15 = 10 m

2-Dimensional Example

Splat the cat walks 5 m north, 15 m west, and 20 m north again.

What is the displacement?

𝑅 = 𝑥2 + 𝑦2

Coordinate Systems and Vector

Components

cos θ =𝑎𝑑𝑗

ℎ𝑦𝑝

sin 𝜃 =𝑜𝑝𝑝

ℎ𝑦𝑝

tan 𝜃 =𝑜𝑝𝑝

𝑎𝑑𝑗

Step 1: make a triangle

Use trig to find x and y

25 m at 30 deg

65 m/s at 250 deg

To Add Multiple Vectors: Example – An airplane flies 190 m/s at 25 degrees above the horizontal

against a wind that is 32 m/s at 30 degrees west of north. What is the

plane’s resultant velocity?

1. Resolve each vector into its components:

2. Total x components:

3. Total y components:

4. Sketch triangle using total x and y

Calculate Resultant:

Calculate angle using trig:

Relative Velocity

What is the velocity of A with respect to B?

Asks what the velocity of A would be, to YOU, if you were

on top of item B

Example: Splat the cat runs east at 3 m/s, while riding on a

train that also travels east at 22 m/s.

Splat’s velocity relative to ground:

Splat’s velocity relative to the train:

What if Splat turned and went west at 3 m/s?

What is his velocity NOW relative to ground:

What about relative to the train?

What if Splat runs north at 3 m/s?

Projectile Motion A projectile is anything that is given initial velocity but then is only

influenced by gravity

Examples: thrown football, tossed basketball, bullet shot from gun, cat

shot from cannon…

Projectiles have parabolic paths

Motion must be broken into x and y components!!

Remember : Gravity only acts in the y – direction!!

Constant Acceleration Projectile – x dir. Projectile – y dir.

𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡

𝑣𝑓2 = 𝑣𝑖

2 + 2𝑎𝑥

𝑥 = 𝑣𝑖𝑡 +1

2𝑎𝑡2

𝑥 =1

2𝑣𝑖 + 𝑣𝑓 𝑡

Modeling Projectile Problems:

1. Always draw a picture

2. Label givens on the picture!

Example: Splat the cat is pushed out of a window that is 35.0

meters above the ground. If Splat lands 6.5 m away from the

building base, how fast was he going when he left the

window?

Step 1: Picture Step 2: Separate Givens into x and y

Step 2: Choose an equation! You cannot mix x and y givens!!!!!!!!

Full Parabola Problems:

1. Always draw a picture

2. Label givens on the picture