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A ship leaves port at noon and has a bearing of S 29° W. If the ship sails at 20 knots, how many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 P.M.?
To find out how many nautical miles south and west the ship will have traveled by 6:00 P.M., we need to calculate the distance the ship has traveled in each direction.
First, let's calculate the total time the ship has been sailing. The ship departs at noon and arrives at 6:00 P.M., which is a time duration of 6 hours.
Next, we need to calculate the distance traveled. To do this, we will use the formula:
Distance = Speed × Time
Given that the ship's speed is 20 knots and the sailing time is 6 hours, we can plug in these values to find the distance traveled by the ship.
Distance = 20 knots × 6 hours = 120 nautical miles
Now we need to break down the distance traveled into south and west components using the given bearing of S 29° W.
Since the bearing is S 29° W, it means the ship is sailing 29° westward of directly south.
To find out the southward distance traveled, we can calculate the sine of the angle using trigonometry:
Southward Distance = Distance × sin(29°)
To find out the westward distance traveled, we can calculate the cosine of the angle using trigonometry:
Westward Distance = Distance × cos(29°)
We can now calculate:
Southward Distance = 120 nautical miles × sin(29°) ≈ 61.81 nautical miles (rounded to two decimal places)
Westward Distance = 120 nautical miles × cos(29°) ≈ 104.95 nautical miles (rounded to two decimal places)
Therefore, by 6:00 P.M., the ship will have traveled approximately 61.81 nautical miles south and 104.95 nautical miles west.
x = -((18-12)*20)sin29°
y = same, but cos29°