A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
In this problem we are faced with an apparently easy area problem,
but it has gone horribly wrong! What happened?
Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.
Explore this idea with the interactivity below . Then scroll
down to see the main challenge.
Things to know :
The graph is not plotting ordinary speed against time, it is
plotting vertical speed or velocity against time. Experiment with
the interactivity until you can predict the graph shape a
particular curve will produce.
This rail is also amazingly smooth - there's no friction or any
other resistance you need to consider.
At the end of a run click on the bead to put it back at the
Also you can drag the bead up the vertical part of the rail to
give it a faster entry onto the curve.
Just experiment and you'll soon see all the things you can
Full Screen Version
Can you shape the rail to produce each graph?
Explain how the features of the graph connect with the bead's
behaviour on the rail. Once you've really "nailed it" why not send
us your solution.
Can you, as an extra challenge, get a drop rate that's
absolutely constant. The vertical velocity stays at one fixed
Send us a screen shot to prove that you did it, plus some text
drawing attention to the qualities of the rail curve that made it