## 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

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?

## Answers ( )

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