A hot air balloon is descending - Edexcel - GCSE Maths - Question 21 - 2020 - Paper 2
Question 21
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... show full transcript
Worked Solution & Example Answer:A hot air balloon is descending - Edexcel - GCSE Maths - Question 21 - 2020 - Paper 2
Step 1
Substituting values for K using heights at 09:15 and 09:16
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Answer
We are given that at 09:15, the height is 1200 metres and at 09:16, it is 1040 metres.
Using the formula:
h_{n+1} = K h_n + 20
Substituting the known values for n = 1 (09:15):
1040 = K * 1200 + 20
Rearranging gives:
K * 1200 = 1040 - 20
K * 1200 = 1020
This leads to:
K = \frac{1020}{1200} = 0.85.
Step 2
Calculating height at 09:17
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Answer
Now we can calculate the height at 09:17 (n = 2) using h_2:
h_2 = K h_1 + 20
h_2 = 0.85 * 1040 + 20
h_2 = 884 + 20 = 904
Therefore, the height at 09:17 is 904 metres.
Step 3
Calculating height at 09:18
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Answer
Next, to find the height at 09:18 (n = 3):
h_3 = K h_2 + 20
h_3 = 0.85 * 904 + 20
h_3 = 768.4 + 20 = 788.4
Thus, the height of the balloon at 09:18 is 788.4 metres.
