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Ball Bearings

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.

Far Horizon

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Air Routes

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.

What's That Graph?

Age 14 to 18
Challenge Level

What's That Graph? printable sheet - graphs
What's That Graph? printable sheet - processes and equations
 

Here are some graphs of physical processes.

   
   
   
   

 

Can you suggest plausible processes that could have given rise to each graph?

Now click on the link below to see eight processes that give rise to the graphs.
Can you match each process to a graph?
 
PROCESSES


Can you suggest equations that could model each of these processes?


Now click on the link below to see eight equations.
Can you match each equation to the graphs and related processes?

EQUATIONS
 

Extension
Can you determine values for the constants A, B and C for each equation? For some, you will need to make some assumptions.
 

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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