1 Chapter 6: Motion in a Plane

2 Position and Velocity in 2-D Displacement Velocity Average velocity Instantaneous velocity Instantaneous acceleration Average acceleration

3 Directions of Instantaneous and average velocities Instantaneous velocity at any point on the curve is along the tangent drawn at that point Average velocity points in the direction of the displacement vector

4 Components of velocity

5 Acceleration (Instantaneous and Average)

6 Equations of Motion in 2-D

7 If a particle’s motion is governed by x=2t 2 and y=5t At any time What would be its displacement, velocity, and acceleration? What would be its speed? What is the angle of inclination? At t = 5 s What would be its position, velocity, and acceleration? Calculate its speed Calculate its angle of inclination θ

8 Projectile Motion A projectile is an object that moves in 2-D under the influence of only the gravitational force For projectiles, a x =0 and a y =-g

9 Components of velocity and acceleration of a Projectile A projectile is launched with an initial velocity (9.8,19.6) m/s Observe that the x- component of velocity is not changing (no change in the length or direction) Vertical component of the velocity is changing in length and direction due to gravitational force!

10 Dynamics of a projectile Projectile motion is made up of two independent motions Uniform motion with constant velocity along x- direction (horizontal) Free-fall motion in the vertical direction

11 Range of a Projectile Range is the longest horizontal distance traveled by a projectile What should be θ for the projectile to have longest range? When would the projectile reach maximum height?

12 Projectile Motion as a function of θ