A ship leaves port at 8 knots (nautical miles per hour) heading \( \mathrm{N} 29^{\circ} \mathrm{W} \). After 2 hr , it makes a \( 90^{\circ} \) clockwise turn to a new bearing of \( \mathrm{N} 61^{\circ} \mathrm{E} \) and travels for 1.5 hr . Part 1 of 2
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In this maritime journey, the ship first moves at 8 knots for 2 hours. That means it covers a distance of \(8 \, \text{knots} \times 2 \, \text{hours} = 16 \, \text{nautical miles}\). The angle \(N 29^{\circ} W\) means that the ship is navigating slightly northwest from the north, which helps us define its position in Cartesian coordinates if we need to plot it later. After 2 hours, with a 90-degree turn to \(N 61^{\circ} E\), the ship is now heading slightly northeast. For 1.5 hours, it will cover an additional distance of \(8 \, \text{knots} \times 1.5 \, \text{hours} = 12 \, \text{nautical miles}\). This change in direction can create some fun geometrical challenges to keep track of the distances traveled in terms of both north-south and east-west components!
