Rollercoaster Distance & Speed

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A roller coaster is built with the following track. The track is made up of straight sections, semi-circle sections and quarter-circle sections.  The coaster climbs slowly to the top of a hill and dangles passengers over a vertical drop before plummeting them downwards through a hole in the ground and returning to the start.

a)  What is the distance that the coaster travels around the track? Round your answer to the nearest metre.

b)  If the ride takes 1 minute 15 seconds from start to finish, what is the average speed of the coaster in MPH? Round your answer to the nearest whole number.

c)  Explain why the average speed is low even though this is a fast ride.

Suggestions:
This question works well to consolidate circumference learning for higher ability students.  It truly tests their accuracy skills and methodical workings as the perimeter of the shape takes concentration and converting units is important to include.  Students take 5-6 minutes to answer this question in full, and it often leads nicely into teaching simultaneous equations with a quadratic.

Teachers could extend the learning by considering:

• The ride design team has stated that for last 80% of the track length the coaster is travelling at 65 mph. What must the speed of the coaster be during the first 20% of the track to account for the average speed given in question b?