Time a courier stays within range of a relay mast
Time a courier stays within range of a relay mast
IP 3
8 marks
A courier rides along a straight road. Her distance, \(s\) km, from a warehouse \(t\) hours after she starts work is modelled by \(s=t^2-6t+13\), for \(0\le t\le 6\). A relay mast stands beside the road \(8\) km from the warehouse. Her phone has signal only when she is within \(3\) km of the mast.
- Explain why she has signal exactly when \(\left|t^2-6t+5\right|\le 3\).[1]
- Find the set of times, in exact form, during which she has signal.[5]
- Find the total length of time for which she has signal, and state one assumption of the model that this answer depends on.[2]
Solution:
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Answer:(b) \(3-\sqrt{7}\le t\le 2\) or \(4\le t\le 3+\sqrt{7}\) (c) \(2\sqrt{7}-2\approx 3.29\) hours
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