## Dumbo Distance & Time

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A theme park ride is of a circular design where guests ride in carriages around a central axis. The diameter of the ride is 15m and guests rotate 5½ times during the ride.

a)  What is the total distance travelled by a guest riding this attraction?

The maximum speed of the carriages on the ride is 12km/hr

b)  How long (in minutes & seconds) does it take to ride this attraction?

Suggestions:
This is a fun question which requires knowledge of circles and speed/distance/time calculations. All formulae for this question need to be recalled and applied by the student. Most students take 3-4 minutes using a calculator, but many students make the error of not converting distance and speed to a consistent distance unit, and therefore get the wrong answer.  It is a good starter or consolidation problem for higher GCSE students, but often needs an extension task for those who know immediately what to do. It often leads to discussions about carriages travelling at different speeds depending on their flying height.

Extension Ideas:

Teachers could extend the learning by considering:

• Some guests choose not to ‘fly’ in dumbo, but stay at ground level just spinning around. Therefore the diameter of their travel is 13.5m instead of 15m. Prove that their speed has been reduced by 10%.
• Instead of ‘flying’, some guests stay at ground level (1 metre vertically below the equator of the ride). How many metres less will they travel in total compare to those flying at the equator of the ride?