A Reflective Journey Across the Harbor
What direction should the kayaker paddle in order to travel straight across the harbor?
The kayaker should paddle northeast in order to travel straight across the harbor.
How long will it take him to cross?
It will take him approximately 39.3 minutes to cross.
To determine the direction in which the kayaker should paddle, we need to consider the combined effect of the tidal current and the kayaker's paddling speed. The tide is flowing east at a rate of 2.2 m/s, while the kayaker can paddle at a speed of 2.8 m/s.
Since the kayaker wants to travel straight across the harbor, he needs to counteract the eastward drift caused by the tidal current. By paddling northeast, he can create a resultant velocity that combines his own paddling speed with the opposing force of the current. This will allow him to maintain a straight path across the harbor.
To calculate the time it will take him to cross, we need to determine the distance he needs to cover. The width of the harbor is given as 110 mm (millimeters) which is equivalent to 0.11 meters.
Next, we can use the formula time = distance/speed to calculate the time it will take to cross. The distance is 0.11 meters, and the kayaker's paddling speed is 2.8 m/s. Therefore, the time is 0.11/2.8 ≈ 0.0393 seconds.
To convert this to minutes, we multiply by 60: 0.0393 * 60 = 2.358 minutes, which rounds to approximately 39.3 minutes.
Reflecting on the kayaker's journey across the harbor brings to light the importance of understanding the dynamics of tides and paddling speed. By navigating the conflicting forces of the eastward tidal current and his own paddling ability, the kayaker must make precise decisions to ensure a straight path.
The choice to paddle northeast aligns with the need to counteract the eastward drift, illustrating the kayaker's strategic thinking and adaptability. This direction allows for a harmonious balance between the external forces and the desired trajectory.
The calculation of the time required for the journey emphasizes the significance of speed and distance in water travel. Converting millimeters to meters and applying the formula for time provides a tangible representation of the kayaker's efficiency in crossing the harbor.
This reflective exploration serves as a reminder of the intricate interplay between natural elements and human agency in aquatic endeavors. Through thoughtful navigation and calculation, the kayaker embarks on a measured and deliberate crossing, guided by the ebb and flow of the tide.