1. Chapter 4:Dynamics: Newton’s Law of Motion
You cannot touch
without being touched-
That’s Newton’s third law!
Read Chapter 4.1 to 4.4 for quiz

2. Vector Kinematics
In two or three dimensions, the displacement is a vector:

3. Vector Kinematics
As Δt and Δr become smaller and smaller, the average velocity approaches the instantaneous velocity.

4. Vector Kinematics
The instantaneous acceleration is in the direction ofΔ = 2 – 1,
and is given by:

5. Vector Kinematics
Using unit vectors,

6. Problem 17
(I) The position of a particular particle as a function of time is given by
Determine the particle’s velocity and acceleration as a function of time.

7. Example 3-5: Position given as a function of time

8. Vector Kinematics
Generalizing the one-dimensional equations for constant acceleration:

9. Projectile Motion
A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola.

10. 2D motion = two independent 1D motions
Figure from “Conceptual Physics for Everyone”, Paul G. Hewitt, Addison Wesley, 2002.

11. Projectile Motion
It can be understood by analyzing the horizontal and vertical motions separately.
The speed in the x-direction is constant; in the y-direction the object moves with constant acceleration g.

12. Projectile Motion
This photograph shows two balls that start to fall at the same time. The yellow ball has an initial speed in the x-direction. The vertical positions of the two balls are identical at identical times, while the horizontal position of the yellow ball increases linearly.

13. X and Y are Independent Red ball is dropped vix=viy=0
White ball is tossed horizontally viy=0 vix≠0
Yellow lines show equal
time intervals .

14. Solving Problems Involving Projectile Motion
Example 3-6: Driving off a cliff.
A movie stunt driver on a motorcycle speeds horizontally off a 50.0-m-high cliff. How fast must the motorcycle leave the cliff top to land on level ground below, 90.0 m from the base of the cliff where the cameras are? Ignore air resistance.

15. Projectile Motion
If an object is launched at an initial angle of θ0 with the horizontal, the analysis is similar except that the initial velocity has a vertical component.

16. Projectile Motion
ay=g
ax=0 y v0
v0y
v0y 
vix x

17. Solving Problems Involving Projectile Motion
Projectile motion is motion with constant acceleration in two dimensions, where the acceleration is g and is down.

18. Problem 31
(II) A fire hose held near the ground shoots water at a speed of 6.5 m/s. At what angle(s) should the nozzle point in order that the water land 2.5 m away (Fig. 3–40)? Why are there two different angles? Sketch the two trajectories. R

19. Solving Problems Involving Projectile Motion
Example 3-7: A kicked football.
A football is kicked at an angle θ0 = 37.0°with a velocity of 20.0 m/s, as shown. Calculate (a) the maximum height, (b) the time of travel before the football hits the ground, (c) how far away it hits the ground, (d) the velocity vector at the maximum height, and (e) the acceleration vector at maximum height. Assume the ball leaves the foot at ground level, and ignore air resistance and rotation of the ball.