Problem 15.2. A nautical mile is a unit of distance frequently used in ocean navigation. It is defined as the length of an arc s along a gre

Question

Problem 15.2. A nautical mile is a unit of distance frequently used in ocean navigation. It is defined as the length of an arc s along a great circle on the earth when the subtending angle has measure 1′ = “one minute” = 1/60 of one degree. Assume the radius of the earth is 3,960 miles.

(a) Find the length of one nautical mile to the nearest 10 feet.

(b) A vessel which travels one nautical mile in one hours time is said to have the speed of one knot; this is the usual navigational measure of speed. If a vessel is traveling 26 knots, what is the speed in mph (miles per hour)?

(c) If a vessel is traveling 18 mph, what is the speed in knots?

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Eloise 2 days 2021-10-11T17:00:51+00:00 1 Answer 0

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    2021-10-11T17:02:21+00:00

    Answer:

    a) 6080 ft

    b) 29.952 mph = 30 mph to 2s.f

    c) 15.6 knots

    Step-by-step explanation:

    Length of an arc is given as (θ/360) × (2πr)

    For a nautical mile, θ = 1′ = (1/60)° = 0.01667°

    Length of a nautical mile = (0.01667/360) × (2π × 3960) = 1.152 miles

    1 mile = 5280 ft

    1.152 miles = 5280×1.152 = 6082.1 ft = 6080 ft to the nearest 10 feet.

    b) 1 knot = 1 nautical mile/hour

    1 nautical mile/hour = 1.152 miles/hour (from part (a))

    1 knot = 1.152 miles/hour

    26 knots = 26 × 1.152 miles/hour = 29.952 mph = 30 mph to 2 s.f

    c) 1.152 mph = 1 knot

    18 mph = (18×1/1.152) knots = 15.625 knots

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