How to Cross a Harbor: A Kayaker's Challenge

Question:

1) In which direction should the kayaker paddle to travel straight across the harbor?

2) How long will it take the kayaker to cross?

Answer:

The kayaker should paddle at approximately 33.7 degrees north of east to travel straight across the harbor.

The kayaker should paddle in a direction that combines his own velocity with the velocity of the tidal current to cancel out their effects. By paddling at an angle of approximately 33.7 degrees north of east, the kayaker can achieve this.

To find this direction, we need to consider the kayaker's velocity of 3.0 m/s to the north and the tidal current velocity of 2.0 m/s to the east. By using trigonometry and vector addition, we can determine the optimal angle for the kayaker to paddle.

The resultant velocity that the kayaker needs to achieve is perpendicular to the direction of the tidal current, which can be calculated using the inverse tangent function:

tanθ = 2.0 m/s / 3.0 m/s

θ = arctan(2.0/3.0) ≈ 33.7 degrees

Therefore, by paddling at approximately 33.7 degrees north of east, the kayaker will be able to travel straight across the harbor and counteract the effects of the tidal current.