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The speed of a small jet aircraft was measured every 5 seconds, starting from the time it turned onto a runway, until the time when it left the ground - Edexcel - A-Level Maths Pure - Question 4 - 2019 - Paper 2
Question 4
The speed of a small jet aircraft was measured every 5 seconds, starting from the time it turned onto a runway, until the time when it left the ground. The results ... show full transcript
Worked Solution & Example Answer:The speed of a small jet aircraft was measured every 5 seconds, starting from the time it turned onto a runway, until the time when it left the ground - Edexcel - A-Level Maths Pure - Question 4 - 2019 - Paper 2
Step 1
(b) explain whether your answer to part (a) is an underestimate or an overestimate of the length of runway used by the jet to take off.
Answer
In part (a), we estimated the length of the runway to be 375 m, using the trapezium rule. It's essential to analyze the nature of the speed data.
The speed of the jet is increasing throughout the 25 seconds, which indicates that the jet is accelerating. In this case, since we used the trapezium rule, we averaged the speeds over each interval.
Because the speed is continually increasing, the actual area under the curve would be greater than the trapezium estimate. Therefore, our answer in part (a) underestimates the distance used by the jet to take off.
Thus, the answer to part (b) is that the estimate is an underestimate of the length of runway used by the jet to take off.