The Falling Ladder

What does it feel like at the top of a ladder as the bottom starts to slide away?

If the bottom slides at a steady rate, do you also fall steadily?

If not, then when do you fall fastest?

Can you see that TWO models are actually needed? One for when the ladder is overhanging the top of the wall, and a second when it passes the top of the wall and begins to fall straight down.

Move the point D to explore this model and to answer questions 1 and 2 below.

 

Before beginning the assessment task, you should activate the GeoGebra CAS engine - press the Activate CAS button which follows until you get a correct result. It may take a couple of attempts. Then commence the task.

 

  

Back to Top

 
 

Assessment

Be sure you have activated CAS before you begin.

Hint: When entering mathematical expressions in the math boxes below, use the space key to step out of fractions, powers, etc. On Android, begin entry by pressing Enter.

Type simple mathematical expressions and equations as you would normally enter these: for example, "x^2[space]-4x+3", and "2/3[space]". For more interesting elements, use Latex notation (prefix commands such as "sqrt" and "nthroot3" with a backslash (\)): for example: "\sqrt(2)[space][space]". More?

 

1. If the ladder is leaning AGAINST the wall (no overhang), then drag the point D above to find the height of the top of the ladder when x = 5?

 

Jump to GeoGebra

 

2. If the ladder is overhanging the top of a wall of height 4 m, then drag the point D to find the height of the top of the ladder above the ground when x = 3?

 

Jump to GeoGebra

 

3. Calculate the length of the overhang from the top of the wall to the top of the ladder when x = 3? (Give numeric answer only)

 

Jump to GeoGebra

 

4. We will begin by building an algebraic model for the height of the top of the ladder from the ground as the ladder slides down the wall - no overhang: height(x) =

 

Jump to GeoGebra

 

5. Next, build an algebraic model for the length of the overhang: overlength(x) =

 

Jump to GeoGebra

 

6. How might you use similar triangles to define the height of the top of the ladder overhanging the wall with respect to x? overhang(x) =

 

Jump to GeoGebra

 

Go back to the graph above and drag the point D - does this verify your results? How difficult did you find this activity? Please assign a rating value from 1 (very easy) to 5 (extremely difficult). Comments? Suggestions? What did you learn from this activity?

 

Jump to GeoGebra

 

My name:

My class:

Teacher Email:

Scan me!
Send to Cloud

Back to Top

Steve Arnold, 17/06/2006, Created with GeoGebra

This problem may also be modelled using CabriJr on the TI-83/84 series calculator. Click on the graphic below to download the file and try it yourself!

Try having students work in pairs: one generating data points using the CabriJr model and the partner entering these into lists to plot and then to help build their algebraic model!

And just wait until you try this with TI-nspire CAS!

©2019 Compass Learning Technologies ← Live Mathematics on the Web ← GeoGebra Showcase ← The Falling Ladder