If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Find the distance of the shortest air route at an altitude of 6000
metres between London and Cape Town given the latitudes and
longitudes. A simple application of scalar products of vectors.
This problem invites students to take a look at the amazing limits that athletes push themselves and their equipment to in search of Olympic glory.
In order to come up with answers, students will need to undertake some research, calculate with measurements and different units, and make comparisons.
For younger students, concentrate on the first few questions dealing with speed, distance and time. Older students studying mechanics and physics may be interested to explore questions on acceleration, stresses and strains.
"What Olympic records do you know about? Do you know who holds the record, and what it is?" Students will share their knowledge of Olympic events and records.
"What if we wanted to make an Alternative Olympic or Paralympic Record Book? For example, we might want a record for the event where a human travels the fastest. Talk to your partner and suggest which event might hold this record."
Give students a couple of minutes to discuss, and then collect their suggestions on the board. If everyone suggests that it must be e.g. Usain Bolt running the 100m, invite them to consider some other possibilities:
If students reject cycling/wheelchair as they include extra equipment, suggest that they might have two categories in their record book, for fastest unaided human and for fastest aided human.
"You'll need to do some research to determine for sure which one of these would get the record."
Perhaps invite students to suggest some other categories for their record books, or offer them the ones from the problem. Then allow them time for research in groups, either to research one question of their choice or a range of questions.
Finally, each group can produce their own 'Alternative Record Book' or if each group has worked on one question, their work could be compiled into a class Record Book.
Which events are likely candidates?
Have you taken a look at the list of Olympic events to check that you haven't missed any out?
What research and calculations will you need to carry out in order to compare the speeds and distances in different events?
The later questions on forces, stress, strain and acceleration require the use of more advanced mathematics, and may prompt students to think of their own challenging follow-up questions.
To get students thinking about measurements and units at the Olympics, start with Olympic Measures.