A hot air balloon is descending - Edexcel - GCSE Maths - Question 20 - 2020 - Paper 2
Question 20
A hot air balloon is descending.
The height of the balloon n minutes after it starts to descend is h_n metres.
The height of the balloon (n + 1) minutes after it sta... show full transcript
Worked Solution & Example Answer:A hot air balloon is descending - Edexcel - GCSE Maths - Question 20 - 2020 - Paper 2
Step 1
Substituting values
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Answer
From the problem, we know that:
At 09:15, the height of the balloon is 1200 metres when n = 0 (h_0).
At 09:16, the height of the balloon is 1040 metres when n = 1 (h_1).
Let’s substitute into the equation:
h_{1} = K h_{0} + 20
Substituting the known values:
1040 = K × 1200 + 20.
Step 2
Finding K
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Answer
Rearranging the equation gives:
1040 - 20 = K × 1200
1020 = K × 1200
Now, solve for K:
K = \frac{1020}{1200} = 0.85.
Step 3
Finding height at 09:17
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Answer
Now that we have K, we can find the height at 09:17 (n = 2).
Using the previous height (h_1 = 1040 metres):
