New Text

x vs. t

y vs. t

Cdrag

+/-

Data 2:

ay (m/s2)

t (s)

ax vs. t

Fair-x (N)

ax (m/s2)

y vs. x

Data 2

Close

3

Axis Convention: The + y-direction is defined as up.  ∆time (s): indicates the time increment at which calculations are performed. Smaller values mean greater accuracy but more data. Init. Height (m): the object must start above the ground. The initial height indicates the distance above the ground when t = 0.0 seconds. Init. Speed (m/s): indicates the speed of the object at t = 0.0 seconds. Launch Angle (°): the object can be dropped from rest ()°), projected horizontally (0°), or projected upward (>0°) or projected downward (<0°) at an angle. g (N/kg): choose a value for the gravitational field constant. Run your experiment on Earth or take a field trip to your favorite planet. Enter as negative. Mass (kg): identify the mass of your object. Profile Area (m2): this is the cross-sectional area of the object.  Drag Coefficient: this unit-less coefficient provides a measure of how efficiently the air streams around the object. Use the Wikipedia page to assist in obtaining an estimated value for your object. Air Density (kg/L): the density of air through which the object is falling. The program assumes this value to be constant. Use the Wikipedia page to provide an estimated value. Additional information is available at our website. Tap anywhere to close.

This is the top of the table.

This program models the motion of an airborne object in the presence of air resistance. Parameters can be changed and their effect on the motion is immediately observed. The currently used parameter values are listed above. The Change Parameters button allows you to modify values. There are two “outputs” - data and graphs. Use the Up and Down arrows to scroll through the data. Look for patterns in the data, inspecting multiple columns for the same time period. The View Data and View Graphs buttons can be used to toggle between the two display outputs. There are two different Data tables. There are multiple graph options. Use the buttons to the right of the graph to alter the quantities being graphed. Sometimes a value of -0.000 is reported. This usually means the value is something like -0.000352 and the last digits are not displayed. The ∆t value is an important parameter. A large value (0.05 and greater) results in inaccuracies (especially for low initial heights). Too small of a (0.01 and smaller) results in excessive amounts of data (especially for tall initial heights or fast initial speeds). For initial heights greater than 1000 m, a value of 0.1 works well. For initial heights less than 100 m, a value of 0.01 or smaller works well. Values of the drag coefficient should be estimated based on object shape. The Wikipedia page is a good resource for making an estimate.

hideHolders

Data 1:

Parameters:

∆t (s)

Change Parameters

Data 1

vi (m/s)

View Graphs

g (N/m)

∆time (s):

m (kg)

Axis Convention:

hi (m)

g (N/kg):

x (m)

Parameters

Up is + … Down is -

vx (m/s)

Quantity:     Value

vy (m/s)

Change

Init. Height (m):

A

View Wikipedia page for guidance.

Mass (kg):

Constraints

0

Air  Dens. (kg/L):

Minimum Value: 0.001 s

y (m)

C

Must be > 0 m

Init. Speed (m/s):

Notice Sign!!

Launch Angle (°):

Values for the following parameters are required to model an air-borne object. Enter the values directly into the field OR tap on the Number Pad icon to use our built-in number entry pad. Tap the Info icon (above right) for information about their meaning. When all values have been entered, tap on the Model Motion button.

vy vs. t

Profile Area (m2):

Use a + value. Indicated direction using angle.

Model Motion

9

Use a - value … since gravity is downward.

Use 0° for horizontal. Use a - value for below horizontal.

Minimum Value: 0.2 kg

ay vs. t

8

Drag Coefficient:

Fair-x vs. t

Must be > 0 m2

1

Θ (°)

Fair-y vs. t

vx vs. t

7

6

Once done, tap the Close button.

View Wikipedia page for guidance.

Fair-y (N)

Close

4

5

A (m2)

.

Use the Number Pad to enter the value of ...

dens (kg/L)

Back Space

2

View:

Trajectory

Model the real-world motion of an air-borne object in the presence of air resistance. Identify and modify parameters and explore a What if …? question.

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