Mastering Tidal Currents: A Kayaker's Guide

A kayaker needs to paddle north across a 100-m-wide harbor

A kayaker is faced with the challenge of paddling across a 100-meter-wide harbor. The tide is going out, creating a tidal current that flows to the east at a speed of 2.0 m/s. The kayaker, on the other hand, can paddle with a speed of 3.0 m/s. In which direction should he paddle in order to travel straight across the harbor? How long will it take him to cross?

Answer:

41.8° to the vertical (west of North), 44.6 s

Explanation:

Using Pythagoras theorem, we can calculate the direction and time taken for the kayaker to cross the harbor:

Let vs be the speed of the stream, vh be the speed in the direction the kayaker must go, and vd be the speed going directly north.

Using the equation: vh² = vs² + vd², where vs = 2 m/s and vh = 3 m/s.

Substitute the values: 3² = 2² + vd²

Solve for vd: vd = √(3² - 2²) = √5 ≈ 2.24 m/s

The direction the kayaker should paddle is given by θ = tan⁻¹(2 / 2.24) ≈ 41.8° to the vertical (west of North).

The time taken to cross the harbor can be calculated as t = distance / vd = 100 / 2.24 ≈ 44.6 seconds.

It can be challenging for a kayaker to navigate through a harbor with a strong tidal current, as the current can impact the kayaker's direction and speed. Proper understanding of the tidal currents and effective paddling techniques are crucial for safely crossing such harbors.