GXWeb The Falling Ladder

©2019 Compass Learning Technologies ← Live Mathematics on the Web ← Geometry Expressions Showcase →The Falling Ladder
The Falling Ladder
Saltire Software, home of Geometry Expressions and GXWeb
Download a Geometry Expressions Model for The Falling Ladder
Try this activity with TI-Nspire™
Symbolic computations on this page use Nerdamer Symbolic JavaScript to complement the in-built CAS of GXWeb

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.
If you were at the top of the ladder and the base began to slide away from the wall, at what point would you be falling fastest?
In this model, the ladder is 6 metres in length, and the wall is 4 metres high.
Move the point X to explore this model and to answer questions 1 and 2 below.

Assessment

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 set the point X above to find the height of the top of the ladder when x = 5?

Jump to model
Jump to GXWeb

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

Jump to model
Jump to GXWeb

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 model
Jump to GXWeb

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. (Before you enter your function, you might go back to the model above and see how well it describes the movement of point P). height1(x) =

Jump to model
Jump to GXWeb

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

Jump to model
Jump to GXWeb

6. You might use similar triangles to define the height of the top of the ladder overhanging the wall with respect to x. (Before you enter your function, go back to the model above and see how well it describes the movement of point P). height2(x) =

Jump to model
Jump to GXWeb

7. Study the trace plots for the falling ladder above. If you are on top of the ladder, then you are falling fastest when x =

Jump to model
Jump to GXWeb

Go back to the graph above and set the point X - 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 model
Jump to GXWeb

My name:

Enter your name:
My class:
Teacher Email:

Back to Top

Back to Model

Share Your Results

The Falling Ladder

Assessment

Share Your Results

Construct your own Model with GXWeb