Whoosh

A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?

Dam Busters 1

At what positions and speeds can the bomb be dropped to destroy the dam?

Dam Busters 2

Can you work out which of the equations models a bouncing bomb? Will you be able to hit the target?

Model Solutions

Stage: 5 Challenge Level:

A shot-putter puts her 4kg shot at some fixed angle and a known, fixed speed; it flies through the air and lands.

The motion is modelled several times according to each of the following assumptions:

1. g is constant, there is no air resistance, the shot is modelled as a point mass.
2. g is constant, it is a still day with low humidity and the radius of the physical shot is taken into consideration.
3. g is constant, it is a misty, still day and the radius of the physical shot is taken into consideration.
4. g is variable, there is no air resistance and the radius of the physical shot is taken into consideration.
5. g is variable, there is no air resistance, the shot is a point mass.
6. g is constant, it is quite blustery and the radius of the physical shot is taken into consideration.

In each case it is assumed that the ground is flat and horizontal.

Based on these modelling assumptions, can you put into order the distances travelled by the shot in each case before it first strikes the ground? What about the times of travel? Are there any that you cannot put in order without more information?

Can you think of any other modelling assumptions which might affect the results?

If you wanted to break the world record for the shot put, in what conditions would you try to do it?

Does the relative importance of these modelling assumptions change for striking a golf ball or hitting a table tennis ball?

NOTES AND BACKGROUND

Mechanics is all about things moving. In reality, any moving object is subject to a bewildering complexity of forces and is composed of a similarly bewildering complexity of constituent pieces. So, we make modelling assumptions. Rather beautifully, these modelling assumptions can reduce aspects of physics to a very simple set of equations which nevertheless produce strikingly accurate and predictive results. Knowing which modelling assumptions are safe and reasonable to make is a skill, and to develop this skill we need to understand how modelling assumptions impact the solution to a problem.

Read our article on modelling assumptions if you are interested in finding out more mathematical details.