(Suitable for CAS extension)
What does it feel like to be at the top of a ladder as the bottom begins to slide away? Do you fall at a steady rate? If not, then what is the nature of your motion - and when are you falling fastest? This modelling problem is suitable for students across the secondary school, from consolidation of work on Pythagoras' Theorem in the early years, to optimization using differential calculus in the senior years.
Before the Activity
Some early work using concrete models (such as rulers or lengths of timber) and motion detector would be useful here.
During the Activity
Challenging tasks such as this are usually best attempted in groups of two or more.