Class 8: Relative velocity and projectile motion Vector operations - - PowerPoint PPT Presentation

Class 8: Relative velocity and projectile motion

Vector operations without a coordinate system

Addition and subtraction of vectors Addition: Subtraction: A B A B ‐B

Sine and cosine rules A B a b c

C cos 2ab

• b

a c B cos 2ac

• c

a b A cos 2bc

• c

b a

2 2 2 2 2 2 2 2 2

     

C Cosine rules: Sine rules:

c C sin b B sin a A sin  

Relative velocity

Velocity of B relative to A = Velocity of B relative to M – Velocity of A relative to M VB rel A = VB rel M – VA rel M Or in simpler but less careful language: Velocity of B relative to A = Velocity of B – Velocity of A VB rel A = VB – VA

Vector equations

t a 2 1 t v r r t a a 2 1 t v v y x y x

2 i i f 2 y x yi xi i i f f

                                          

For constant acceleration motion (2D): y x

2

at 2 1 t vi

f

r ri 

Equations of motion

t a v v t a 2 1 t v y y : g)

• r

g (a s coordinate

• y

v v t v x x : 0) (a s coordinate

• x

y iy y 2 y iy i y ix x ix i x

         

y x O g 

Projectile motion is a constant acceleration motion (2D). Acceleration vector is perpendicular towards ground. Correct only if the x‐axis is parallel to ground, because we have assume ax=0.

Example 1

t a v v t a 2 1 t v y y : g)

• r

g (a s coordinate

• y

v v t v x x : 0) (a s coordinate

• x

y yi y 2 y iy i y xi x ix i x

         

y x O g  R=?