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The heptathlon is an athletics contest made up of seven events - Scottish Highers Maths - Question 10 - 2022

Question 10

The heptathlon is an athletics contest made up of seven events. Athletes score points for each event. In the 200 metres event, the points are calculated using the fo... show full transcript

Worked Solution & Example Answer:The heptathlon is an athletics contest made up of seven events - Scottish Highers Maths - Question 10 - 2022

Step 1

Calculate how many points would be awarded for a time of 24.55 seconds in the 200 metres event.

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Answer

To find the points awarded for a time of 24.55 seconds, substitute $T = 24.55$ into the formula:

$P = 4.99087(42.5 - 24.55)^{1.81}$

Calculating the difference:

$42.5 - 24.55 = 17.95$

Now substituting back into the formula:

$P = 4.99087(17.95)^{1.81}$

Calculating $(17.95)^{1.81} \approx 1096.1763$ , thus:

$P \approx 4.99087 \times 1096.1763 \approx 5486.4$

Rounding to two significant figures:

$P \approx 929$

Step 2

Given that 850 points are awarded for a jump of 600 cm, calculate the value of k.

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Answer

Using the points formula for the long jump:

$850 = 0.188807(600 - 210)^{k}$

First, calculate $D$ :

$600 - 210 = 390$

Substituting this in:

$850 = 0.188807(390)^{k}$

Now, isolate $(390)^{k}$ :

$\frac{850}{0.188807} = (390)^{k}$

Calculating the left side:

$\frac{850}{0.188807} \approx 4502.34$

Taking logarithm on both sides:

$k \log(390) = \log(4502.34)$

Now solving for $k$ :

$k = \frac{\log(4502.34)}{\log(390)} \approx 1.41$

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