Comment:
Migration of unmigrated content due to installation of a new plugin
Composition Setup
Image Added
Photo by Craig Kinzer, courtesy Wikipedia.
The Piper Tomahawk, widely used for flying lessons, has a liftoff speed of about 55 knots and a landing speed of about 46 knots. The listed ground-roll for takeoff is 820 feet, and for landing is 635 feet.
Excerpt
hidden
true
In this example we will calculate acceleration, time, speed, and distance assuming constant acceleration.
Deck of Cards
id
partdeck
Card
label
Part A
Part A
Assuming constant acceleration, what is the Tomahawk's acceleration during the takeoff run?
Solution
Toggle Cloak
id
sysa
System:
Cloak
id
sysa
In each of the parts, we will treat the Tomahawk as a point particle.
Toggle Cloak
id
inta
Interactions:
Cloak
id
inta
We are assuming that the thrust from the plane's engine, air resistance, rolling friction, and all other influences add up to give a constant acceleration.
Toggle Cloak
id
moda
Model:
Cloak
id
moda
One-Dimensional Motion with Constant Acceleration.
Toggle Cloak
id
appa
Approach:
Cloak
id
appa
Card
Part A
Part A
Card
label
Part B
Part B
What is the elapsed time from the instant the plane begins its takeoff run until it lifts off the ground?
Solution
System, Interactions and Model: The system, interactions and model are the same as in Part A.
Toggle Cloak
id
appb
Approach:
Cloak
id
appb
Card
Part B
Part B
Card
label
Part C
Part C
How far does the plane travel in the first 9.0 seconds of the takeoff?
Solution
System, Interactions and Model: As in the previous parts.
Toggle Cloak
id
appc
Approach:
Cloak
id
appc
Card
Part C
Part C
Card
label
Part D
Part D
What is the acceleration during landing?
Solution
System, Interactions and Model: As in the previous parts.
Toggle Cloak
id
appd
Approach:
Cloak
id
appd
Card
Part D
Part D
Card
label
Part E
Part E
How far does the plane travel in the first 9.0 seconds of the landing?
Solution
System, Interactions and Model: As in previous parts.
Toggle Cloak
id
appe
Approach:
Cloak
id
appe
Card
Part E
Part E
Deck of Cards
partdeck
partdeck
Wiki Markup
{table:align=right}{tr}{td}!tomahawk_craigKinzer.jpg!{td}{tr}{tr}{td}(Photo by Craig Kinzer, courtesy Wikipedia.){td}{tr}{table}
The Piper Tomahawk, widely used for flying lessons, has a liftoff speed of about 55 knots and a landing speed of about 46 knots. The listed ground-roll for takeoff is 820 feet, and for landing is 635 feet.
h3. Part A
Assuming constant acceleration, what is the Tomahawk's acceleration during the takeoff run?
System: In each of the parts, we will treat the Tomahawk as a point particle.
Model: [One-Dimensional Motion with Constant Acceleration|1-D Motion (Constant Acceleration)].
Approach: Once we have determined that we are using 1-D Motion with Constant Acceleration, we have essentially reduced the problem to math. The Constant Acceleration model is somewhat unique in that there is an overabundance of equations (Laws of Change) to choose from. In order to select the proper equation or equations, we have to clearly understand the information presented in the problem (often called the _givens_) and also what we are asked to find (the _unknowns_).
To understand our givens, it is a good idea to first develop a coordinate system. By drawing out the runway and marking where the plane starts its take-off run (x = 0 feet in the picture) and where it lifts off the ground (820 feet in the picture) we can see that the 820 feet given in the problem statement is a _distance_ not a position. The difference between the plane's liftoff position and the starting point is 820 feet.
!runway1.png!
h3. Part B
What is the time required for takeoff?
h3. Part C
How far does the plane travel in the first 1.0 seconds of the takeoff?
h3. Part D
What is the acceleration during landing?
h3. Part E
How far does the plane travel in the first 1.0 seconds of the landing?
h3. Part F
Suppose that the Tomahawk was landing in a tailwind of 5 knots, so that it actually approached the runway moving at 51 knots along the ground instead of 46 knots. How much distance would the plane require to stop?
