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?

Question

Mathematics

Leo Vance

11 September, 17:09

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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Answers (1)

Know the Answer?

Xzavier Butler · Answer 1

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