Topics: Length, Ratio, Earthquake engineering Pages: 2 (450 words) Published: February 12, 2012
• Using a spreadsheet, or geometric software, simulate the positions of the two runners for a variety of values of the speeds u and v , the time t and the distance d . • Using the data generated above, discuss the condition(s) necessary for Buddy to catch up with Angie. Again, include estimates for: o the time at which Buddy catches up with Angie. o the distance travelled by each runner when Buddy catches up. • Discuss the assumptions in the above model. What limitations does it have when applied to other situations?

For final assessment in 2011 and 2012

–8–

MATHL/PF/M11/N11/M12/N12

MODELLING A FUNCTIONAL BUILDING

HL TYPE II

To the student: The work that you produce to address the questions in this task should be a report that can stand on its own. It is best to avoid copying the questions in the task to adopt a “question and answer” format. As an architect you have been contracted to design a building with a roof structure similar to the one shown below.

In this task you are to model such a building and produce a report to the contractor with all necessary specifications.

(This task continues on the following page)
For final assessment in 2011 and 2012

–9–

MATHL/PF/M11/N11/M12/N12

You are to design an office block inside a structure with the following specifications: The building has a rectangular base 150 m long and 72 m wide. The maximum height of the structure should not exceed 75 % of its width for stability or be less than half the width for aesthetic purposes. The minimum height of a room in a public building is 2.5 m. • Create a model for the curved roof structure when the height is 36 m. • Find the dimensions of the cuboid with maximum volume which would fit inside this roof structure. • Use technology to investigate how changes to the height of the structure affect the dimensions of the largest possible cuboid. • For each height, calculate the ratio of the volume of the wasted space to the volume of the office block....