How to Cross a Harbor with Tidal Current Using Kayak

What is the best direction for the kayaker to paddle in order to travel straight across the harbor?

a) 48.2 degrees north of west

How long will it take for the kayaker to cross the harbor?

b) 44.72 seconds

Answer:

a) 48.2 degrees north of west

b) 44.72 seconds

Explanation:

In order to travel straight across the harbor, the kayaker's horizontal component velocity must be the same magnitude and opposite direction as the tidal velocity, which is 2.0 m/s to the east. Therefore, the kayaker should paddle at a speed of 2.0 m/s westward.

For the direction (a):

cos α = 2/3

α = cos^-1(2/3) = 0.841 radians = 48.2 degrees north of west

For the time (b):

The kayaker's vertical component of velocity would be √(3^2 - 2^2) = √5 = 2.24 m/s

Therefore, the time it takes for the kayaker to cross the 100m wide harbor at a rate of 2.24 m/s is 100 / 2.24 = 44.72 seconds.