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'Cannon Balls' printed from https://nrich.maths.org/
Why do this problem?
This short problem is a reasonably routine application of
kinematics; the interest lies in the numbers obtained and the
questions concerning the validity of a physical model of constant
gravitational force.
Possible approach
Students could be asked to make an estimate of the speeds and
heights before starting the calculation. Developing a skill and
habit for estimation is very useful in more advanced applications
of mathematics.
Key questions
- What has the radius of the earth got to do with this
problem?
Possible extension
You could also extend this
to suppose that the balls are fired upwards on a
trampoline with coefficient of restituion 0.5. How many bounces
would it take for each ball to bounce less than 1m high?
Possible support
Provide students with the equation for motion under a constant
force.