Succeed with maths – Part 2
Succeed with maths – Part 2

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Succeed with maths – Part 2

3.4 Formulas in archaeology

Footprints from prehistoric human civilisations around the world have been found preserved in either sand or volcanic ash. From these tracks, it is possible to measure the foot length and the length of the stride. These measurements can be used to estimate both the height of the person who made the footprint and also whether the person was walking or running. This can be done by using three formulas:

height equation left hand side equals right hand side seven postfix multiplication length of foot

relative stride length equation left hand side equals right hand side stride length divided by hip height

hip height equation left hand side equals right hand side four postfix multiplication length of foot

Note that no units have been included in these formulas – so it is important to make sure that you use the same units, such as centimetres, throughout the calculation.

The formula for relative stride length is used to establish if the person was walking or running. If the value of the relative stride length is less than 2, the person was probably walking; if the value is greater than 2.9, the person was probably running. Between these two values, it is difficult to be sure if the person was running or walking. The expected value for relative stride length is usually between 0 and 5.

Notice that the relative stride lengths quoted have no units. The stride length and the hip height are both measured in cm, and when one is divided by the other, these units cancel each other out, just like cancelling numbers when dealing with fractions. If you go on to study physics or other sciences, you will find many examples like this.

Before trying the next activity, if you would like to see one of these formulas being used in practice, have a look at this short video [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

Activity 10 Footprints in the sand

Timing: Allow approximately 10 minutes

From one set of footprints, the length of the foot is measured as 21.8 cm and the stride length as 104.6 cm. What does the data suggest about the height and the motion of the person who made these footprints? Remember you can click on ‘reveal comment’ if you get stuck.

Comment

Break the problem down into simpler parts. Start by asking yourself what you need to know to tell if the person was running or walking.

Answer

height equation left hand side equals right hand side seven postfix multiplication length of foot

So,

multiline equation row 1 estimated height of the person equals seven multiplication 21.8 cm row 2 equals 153 cm (to the nearest cm).

To work out if the person was running or walking, it is important to know the relative stride length. This is given by:

relative stride length equation left hand side equals right hand side stride length divided by hip height

The question gives the information about the stride length but not the hip height. To calculate the hip height use this formula.

hip height equation left hand side equals right hand side four postfix multiplication length of foot

Fortunately, this can be done, as the foot length is also given in the question.

So, hip height equation left hand side equals right hand side four multiplication 21.8 cm equals 87.2 cm

This has given all the information needed to calculate the relative stride length. So, substituting into the formula:

relative stride equation sequence equals 104.6 divided by 87.2 equals 1.2 (rounded to 1 decimal place).

As the relative stride length is less than 2, the person was probably walking.

This was a slightly more complicated problem than our previous examples as it required a step in the middle to calculate some extra information needed. So, well done for having a go!

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