Chapter 6: Motion in a Plane

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=2t2 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, ax=0 and ay=-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