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**Kinematics in Two Dimensions**

Chapter 3 Kinematics in Two Dimensions

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**3.1 Displacement, Velocity, and Acceleration**

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**3.1 Displacement, Velocity, and Acceleration**

Average velocity is the displacement divided by the elapsed time.

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**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.

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**3.1 Displacement, Velocity, and Acceleration**

DEFINITION OF AVERAGE ACCELERATION

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**3.2 Equations of Kinematics in Two Dimensions**

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**3.2 Equations of Kinematics in Two Dimensions**

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**3.2 Equations of Kinematics in Two Dimensions**

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**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.

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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?

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**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

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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?

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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.)

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**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?

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