Independent Practice

A ball is throw vertically overhead and returns to its starting position after 3.6 seconds.

(a) With what initial velocity was the ball thrown?(b) What is the maximum height reached by the ball?

Thought Experiment

There is an interesting monkey at the zoo. The zookeeper feeds the monkey by shooting

bananas from a banana cannon to the monkey in the tree. This particular monkey has a habit of

dropping from the tree the moment that the banana leaves the muzzle of the cannon. If the

monkey lets go of the tree the moment that the banana is fired, will it catch the banana?

Describe what you believe will happen and why.

Two Dimensional Motion

KEY IDEA: Horizontal motion and Vertical motion are INDEPENDENT of each other.

“Cliff” problems:Vertical Motion: ay = - 9.8 m/s2 (Free – Fall)

Horizontal Motion: ax = 0 m/s2

Kinematics Equations

Horizontal Vertical

Vertical Horizontal

Time ay (m/s2) vy (m/s) y (m) ax (m/s2) vx (m/s) x (m)

0 s - 9.8 0 78.4 0 20 0

1 s - 9.8 - 9.8 73.5 0 20 20

2 s - 9.8 - 19.6 58.8 0 20 40

3 s - 9.8 - 29.4 34.3 0 20 60

4 s - 9.8 - 39.2 0 0 20 80

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

20

25

Time (s)

Hor

izon

tal V

eloc

ity

(m/s

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70

80

90

Time (s)

Hor

izon

tal P

ositi

on (m

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Time (s)

Verti

cal V

eloc

ity

(m/s

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70

80

90

Time (s)

Verti

cal P

ositi

on (m

)

Representing Quantities

Vectors:Remember: Any quantity with magnitude and direction (Displacement, Velocity, Acceleration)Represented by an ARROW, that is proportional in size and direction.

V = 5 m/s EastV = 2 m/s North

Actual Velocity

At t = 2s:

Vx = + 20 m/sVy = - 19.6 m/s

Resultant Vectors

Pythagorean Theorem:= +

Vx

Vy V

Problem Solving

1. Draw a picture and include labels!2. List variables in “x” and “y” directions

SEPERATELY!