Math In The Movies ‐ The Martian Solution Question 1 For this question we first have to find the equivalent sols supply for one person. Since NASA provided the team of 8 crew with food for 90 sols, we can find supply for one person by multiplying by 8: 8 ∗ 90 720 Watney rations out the food to last about 1.25 times longer than normal: ∗
1.25 ∗ 720 900
(1 mark) Watney will need food for another 700 sols (he estimates it will be 1600 sols until rescue). Mark needs 1500 calories per sol. We can calculate the remaining calories required: ∗
700 ∗ 1500 1050000 A single potato has about 130 calories. That means he needs to grow a total of: /
1050000/130 8077(1 mark) Question 2 The circular farm area has a radius of 6.27 metres, so we can calculate the total farming area: ∗ ^2 123.5 ^2 (1 mark) As the floor has a depth of 12 centimetres, total soil required is: ∗
123.5 ^2 ∗ 0.12 14.8 ^3 He calculates that he needs about 35 litres of water per cubic metre. In total he’ll need: ∗
14.8 ∗ 35 518
(1 mark) All material copyright Math Thrills Pty Ltd www.MathThrills.com Question 3 The molecular weights of the various molecules involved help us to calculate that 1 kilogram of oxygen combines with 0.144 kilograms of hydrogen to form 1.144 kilograms of water. Assume that 1 litre of water is the same as 1 kilogram of water. Students can calculate how much oxygen and hydrogen Watney will need to source to generate the required 518 litres of water: ∗
518 ∗ 1/1.144 452.8
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(1 mark) 518 ∗ 0.144/1.144 65.2
(1 mark) Question 4 Mark has 3 square metre solar panels that are 14.5% efficient (they absorb 14.5% of the approximately 800 watts of sunlight hitting each square metre). He has about 11 hours of good sunlight each day to charge these solar panels. A fully charged battery has 20000 watt hours of energy storage. We can calculate how many solar panels he needs to bring along to completely charge this battery: ∗
/
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20000/ 800 ∗ 0.145 ∗ 11 15.67 ^2 15.67/3 5.22 (2 marks) Mark will need to bring along 6 solar panels (5 isn’t quite enough). (1 mark) All material copyright Math Thrills Pty Ltd www.MathThrills.com