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

A. with a component of velocity in the forward direction.

B. straight up.C. with a component of velocity in

the backward direction.

Ch4 Two Dimensional Kinematics4-1 Motion in Two DimensionsA. Constant Velocity

1. vx = v0x vy = v0y

2. x = x0 + v0x t y = y0 + v0y t

P4.2 (p. 101)

B. Constant Acceleration

1. vx = v0x + axt

2. vavx = (v0x + vx) / 2

3. x = x0 + (v0x + vx) t / 2

4. x = x0 + v0x t + axt2/2

5. vx2 = v0x

2 + 2ax(x – x0)

Assuming the initial conditions at t = 0, x = x0 and v = v0x and ax is constant.

1. vy = v0y + ayt

2. vavy = (v0y + vy) / 2

3. y = y0 + (v0y + vy) t / 2

4. y = y0 + v0y t + ayt2/2

5. vy2 = v0y

2 + 2ay(y – y0)

P4.5 (p. 101)

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.

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

A. t1 = t2

B. t1 = 2t2

C. t1 = t2/2

D. t1 > t2

E. t1 < t2

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

Concept Question 3

4-3 Zero Launch Angle

P4.8 (p. 101)

x

yP4.13 (p. 101)

Concept Question 4P4.13c: 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?

A. vx stays the same and vy doubles.

B. vy stays the same and vx doubles.

C. vx and vy both double.

D. vx and vy both stay the same.

x

y

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

4-4 General Launch Angle

P4.29 (p. 103)

Concept Question 5P4.29a: Is the landing speed of snowball A

A. greater than that of snowball B?

B. less than that of snowball B?

C. the same as that of snowball B?

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?

A. rockB. ballC. both have the same speed

Read sample responses to q4-2.

4-4 General Launch Angle

P4.35 (p. 103)

Concept Question 7P4.35b: Which is true about the handball?

A. The handball is below its maximum

height.

B. The handball is at its maximum height.

C. The handball is above its maximum

height.

4-5 Projectile Motion: Key Characteristics

T/2

T/2 - t T/2 + t

T0

The Symmetry of Projectile Motion

The green vectors are velocities.

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

A. nowhereB. the highest pointC. the launch point

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

A. nowhereB. the highest pointC. the launch point

Fig. 4.9, p.85

4-5 Projectile Motion: Key Characteristics

P4.38 (p. 103)

P4.69 (p. 105)

A.

B.

C.

D.

Concept Question 10

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

A. fall behind the cart.

B. fall ahead of the cart.

C. land in the cup.