with a component of velocity in the forward direction. straight up.

1. CT1: Suppose you are running at constant velocity along a level track and you wish to throw a ball so you catch it when it comes back down. You should throw the ball • with a component of velocity in the forward direction. • straight up. • with a component of velocity in the backward direction.

2. Ch4 Two Dimensional Kinematics4-1 Motion in Two DimensionsA. Constant Velocity • vx = v0x vy = v0y • x = x0 + v0x t y = y0 + v0y t • P4.2 (p. 101)

3. B. Constant Acceleration • vx = v0x + axt • vavx = (v0x + vx) / 2 • x = x0 + (v0x + vx) t / 2 • x = x0 + v0x t + axt2/2 • vx2 = v0x2 + 2ax(x – x0)Assuming the initial conditions at t = 0, x = x0 and v = v0x and ax is constant.

4. P4.5 (p. 101) • vy = v0y + ayt • vavy = (v0y + vy) / 2 • y = y0 + (v0y + vy) t / 2 • y = y0 + v0y t + ayt2/2 • vy2 = v0y2 + 2ay(y – y0)

5. 4-2 Projectile Motion Don’t use the derived projectile motion equations. Start from a drawing, listing knowns and unknowns and the constant acceleration equations.

6. 4-2 Projectile Motion • Neglect air resistance • Neglect the Earth’s rotation • Neglect the small variations in g over the Earth’s surface and with height. • ax = 0 and ay = -9.81 m/s2 • CT2: For all the above parabolic trajectories above the time to rise to the maximum height (t1) is related to the time to return to the same level from the maximum height (t2) by • t1 = t2 • t1 = 2t2 • t1 = t2/2 • t1 > t2 • t1 < t2

7. Concept Question 3

8. 4-3 Zero Launch Angle P4.8 (p. 101)

9. y P4.13 (p. 101) x

10. Concept Question 4 • P4.13c: If the speed of the crow doubles, then which of the following statements is true about the components of the velocity just before the clam hits the ground? • vx stays the same and vy doubles. • vy stays the same and vx doubles. • vx and vy both double. • vx and vy both stay the same.

11. P4.16 (p. 102) Which direction do I interrogate to get the time of fall? x y

12. 4-4 General Launch Angle P4.29 (p. 103)

13. Concept Question 5 • P4.29a: Is the landing speed of snowball A • greater than that of snowball B? • less than that of snowball B? • the same as that of snowball B?

14. Before Class Assignment 2/13/2008 • q4-1 17/18 correct • q4-2 4 correct plus correct explanation 14 incorrect or incorrect explanation CT6: A rock is dropped at the same instant that a ball at the same initial elevation is thrown in the horizontal direction. Which will have the greater speed when it reaches the ground? • rock • ball • both have the same speed Read sample responses to q4-2.

15. 4-4 General Launch Angle P4.35 (p. 103)

16. Concept Question 7 • P4.35b: Which is true about the handball? • The handball is below its maximum height. • The handball is at its maximum height. • The handball is above its maximum height.

17. 4-5 Projectile Motion: Key Characteristics

18. The Symmetry of Projectile Motion T/2 T/2 - t T/2 + t 0 T The green vectors are velocities.

19. CT8: A projectile in freefall has a projection angle less than 90°. At what point are the velocity and acceleration parallel? • nowhere • the highest point • the launch point

20. CT9: A projectile in freefall has a projection angle less than 90°. At what point are the velocity and acceleration perpendicular? • nowhere • the highest point • the launch point

21. Fig. 4.9, p.85

22. 4-5 Projectile Motion: Key Characteristics P4.38 (p. 103) P4.69 (p. 105)

23. A. B. C. D. Concept Question 10

24. Cart and Cannon: When I give the cart a shove it moves at constant velocity across the table once it leaves my hand. The pin will pull out and project the ball upward. When the ball returns to its original level, it will • fall behind the cart. • fall ahead of the cart. • land in the cup.