51-FOOT LADDER
the math of climbing things
name date
Act One: The Wallitano
1 OSHA is the government agency responsible for workplace safety. First, read their recommendation for ladders and
summarize it in a way that’s easy to understand. Then, are all of the ladders below positioned safely?
2 Arizona governor Janet Napolitano once said, “You show me a fifty-foot wall, and I’ll show you a fifty-one foot ladder.” Would a 51-foot ladder be long enough to climb a 50-foot wall? Show your work below.
© Mathalicious 2011
3 If you wanted to safely climb a 50-foot wall, what’s the shortest ladder you’d be willing to use? Explain.
4 Two students were overheard making the following comments. Do you agree?
a. “To climb one foot higher, you need the ladder to be one foot longer.”
b. “To climb twice as high, you need the ladder to be twice as long. “

Act Two: (The Roof)3 Is On Fire!
5 Watch the video about Pierce fire trucks. Assuming it follows the OSHA recommendation, what’s the highest floor one
of these apparatus can safely reach, and how far away from the building must it park?
6 Imagine there were a fire on the 25th floor of an office building. For a fire truck to safely evacuate people from this height, how long would the ladder have to be? Do you think Pierce should build this new apparatus?
7 The reason for OSHA’s safe ladder angle has to do with gravity and friction. If a ladder is too steep it can fall backwards; if it’s not steep enough it can slide down the wall. Because of hydraulics, though, fire trucks can position ladders however they want, from perfectly vertical to perfectly horizontal.
Imagine you’re a firefighter riding on the current 100-foot ladder truck. In the space below, sketch the steepest ladder you’d be willing to climb and the highest floor you’d be able to reach. Explain your reasoning.
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