You are steering 107°T, and a light is...

Question 1 of 31048fy_heal_CREATE_q211_2017

You are steering 107°T, and a light is picked up dead ahead at a distance of 11 miles at 0847. You change course to leave the light 3 miles off to starboard. If you are making 15.5 knots, what is your ETA at the position 3 miles off the light?

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Question 1 of 31048

🔍 Key Concepts

• Relative motion of your vessel to a fixed light on the earth • Using speed-time-distance: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$ with proper unit conversions • Right triangle/trigonometry idea: passing a fixed point at a given closest point of approach (3 miles to starboard)

💭 Think About

• First, if the light is 11 miles dead ahead at 0847 and you want to pass 3 miles to starboard, what kind of track relative to the light are you actually following? Straight line past the light, or something else? • Think about the geometry: if you will pass 3 miles abeam of the light, what is the distance from your current position to that closest point of approach, assuming constant speed and a single altered course? • Once you know the steaming distance from your 0847 position to the CPA (3 miles off the light), how many minutes will that take at 15.5 knots, and what clock time does that correspond to?

✅ Before You Answer

• Make sure you convert knots to nautical miles per minute correctly before finding time: 1 knot = 1 NM/hour • Verify that the leg you are timing is from the moment you pick up the light at 0847 until the moment you are 3 miles abeam of the light, not until you are abeam of the light itself • Check that your final ETA makes sense: at 15.5 knots, covering a bit less than 11 miles should take well under an hour from 0847