### 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.