Mathematics, 07.03.2020 05:35 KariSupreme
Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (nautical miles per hour, a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day.
a. Start counting time with t =0 at noon and express the distance s between the ships as a function of t.
b. How rapidly was the distance between the ships changing at noon? One hour later?
c. The visibility that day was 5 nautical miles. Did the ships ever sight each other?
d. Graph s and ds/dt together as functions oft for -1 <= t<= 3, using different colors if possible. Compare the graphs and reconcile what you see with your answers in parts (b) and (c).
e. The graph of ds/dtlooks as if it might have a horizontal asymptote in the first quadrant. This in turn suggests that ds/dt approaches a limiting value as t →[infinity] . What is this value? What is its relation to the ships' individual speeds?
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