Your vessel is on a course of 126°T at 17...

Question 1 of 2707066636ee928f7522a1c51a5aa

Your vessel is on a course of 126°T at 17 knots. At 0251 a light bears 099.5°T, and at 0313 the light bears 081°T. At what time and at what distance off will your vessel be when abeam of the light?

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Question 1 of 27070

🔍 Key Concepts

• Use relative bearings: compare the light’s true bearings to your ship’s true course (126°T) to find how many degrees off the bow the light is at each time. • The light is fixed; your ship is moving in a straight line at constant speed, so the change in bearing over time is uniform along your track (assume no current or course change). • "Abeam" of the light means the bearing of the light is 90° from your heading (on the beam), so find the true bearing that corresponds to 90° off your course.

💭 Think About

• First convert the two observed true bearings to relative bearings from your ship’s head (how many degrees off the bow). How far from the beam (90° off) is each one? • Calculate the rate of change of bearing (degrees per minute) between 0251 and 0313, then extend that trend until the relative bearing becomes 90°. From that, find the time when you’ll be abeam. • Once you know how many minutes it takes from either observation until you’re abeam, use your speed (17 knots) to find distance run in that time, then use the right triangle at abeam to relate this run to the distance off the light.

✅ Before You Answer

• Be sure you compute the time interval between 0251 and 0313 correctly (in minutes). • Check that you are using the correct abeam true bearing: for a course of 126°T, the port and starboard beam bearings differ by ±90°. Choose the one consistent with the observed bearings. • Confirm your units when converting speed and time to distance: 17 knots × time (in hours) = distance (in nautical miles).