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 c b B C a   Cosine rules: 2 2 2 a b c - 2bc cos A   2 2 2 b a c - 2ac cos B   2 2 2 c a b - 2ab cos C Sine rules: sin A sin B sin C   a b c

Relative velocity Velocity of B relative to A = Velocity of B relative to M – Velocity of A relative to M V B rel A = V B rel M – V A rel M Or in simpler but less careful language: Velocity of B relative to A = Velocity of B – Velocity of A V B rel A = V B – V A

Vector equations For constant acceleration motion (2D):         v a x x     1 1                xi x f i 2 2 t t r r v t a t         f i i     v a y y     2 2 yi y f i 1 2 y at v i t 2 r f r i  x 0

Equations of motion y Projectile motion is a constant acceleration motion (2D). g Acceleration vector is perpendicular towards ground.  x O  x - coordinate s (a 0) : x   Correct only if the x ‐ axis is x x v t i ix parallel to ground, because  v v we have assume a x =0. x ix  y - coordinate s (a g or - g) : y 1    2 y y v t a t i iy y 2   v v a t y iy y

Example 1 y g  x O R=?  x - coordinate s (a 0) : x   x x v t i ix  v v x xi  y - coordinate s (a g or - g) : y 1    2 y y v t a t i iy y 2   v v a t y yi y