1. Trial and improvement
[ A3.1 Extension Plenary]
Find the answer to this Ancient Egyptian puzzle to the nearest 0.1. “A number plus its two thirds, plus its half and its seventh makes 37. What is the number?”
This formula gives the power, P watts, from a wind turbine, with rotors radius r metres in a wind of speed v metres per second. (a) A small wind turbine has rotors of 2m radius. What wind speed would be needed to generate 1000 watts? (b) Amy lives near Liverpool where the average wind speed is 5.5 metres per second. What radius wind turbine would she need to generate 1000 watts?
Preamble
Some problems whose solutions are found by trial and improvement. The first
problem could be solved using fractions but it lends itself to trial and improvement.
Using a spreadsheet would be an efficient method of applying trial and improvement
in all the problems. In all cases no hint his given to the possible region the solution
may lie, so children will need to make some rough initial guesses – a useful practice.
Possible content
Using trial and improvement to solve problems.
Resources
Calculator, possibly spreadsheet.
Solution/Notes
Effectively finding by trial and improvement the solution to: So to d.p. a solution is 16.
a) Wind speed of about 9.4 metres per second b) Wind turbine radius of about 4.5 m.
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010