1. Kinematics in Two Dimensions
Chapter 3
Kinematics in Two Dimensions

2. 3.1 Displacement, Velocity, and Acceleration

3. 3.1 Displacement, Velocity, and Acceleration
Average velocity is the
displacement divided by
the elapsed time.

4. 3.1 Displacement, Velocity, and Acceleration
The instantaneous velocity indicates how fast
the car moves and the direction of motion at each
instant of time.

5. 3.1 Displacement, Velocity, and Acceleration
DEFINITION OF AVERAGE ACCELERATION

6. 3.2 Equations of Kinematics in Two Dimensions

7. 3.2 Equations of Kinematics in Two Dimensions

8. 3.2 Equations of Kinematics in Two Dimensions

9. Under the influence of gravity alone, an object near the
3.3 Projectile Motion
Under the influence of gravity alone, an object near the
surface of the Earth will accelerate downwards at 9.80m/s2.

10. Example
A ball thrown horizontally from a 13m high building strikes the ground 5.0m from the building. With what velocity was the ball thrown?

11. Solution By definition, we have y = voyt – ½ gt2 t2 = -2y/g
t = 1.63s
Also, by definition we have
x = voxt + ½ axt2
vox = x/t
= 5/1.63
= 3.07m/s

12. Problems to be solved
3.12, 3.24, 3.41, 3.45, 3.51, 3.72
B3.1 A snowball is thrown from 2m above the ground at a velocity of 10m/s directed at 30° above the horizontal. (a)How long will the snowball be in the air? (b) Where will it land?

13. B3.2 Some books advice serving a tennis ball at an angle below the horizontal direction. To see if this is sound advice, suppose a ball is struck at an angle of 5° downward at a height of 2.4m with the relatively high speed of 30m/s. How high will it be when it reaches the net 12m away? (The net is 0.9m high. Neglect air resistance.)

14. B3. 3 A tennis ball is served 2
B3.3 A tennis ball is served 2.5m above the ground at an angle of 5° above the horizontal direction with an initial speed of 30m/s. (a) When will it hit the ground? (b) How far will it travel?