Question

A kayaker needs to paddle north across a 100 m wide harbor. the tide is going out, creating a tidal current flowing east at 3m/s. the kayaker can paddle with a speed of 4.0m/s. In which direction should he paddle in order to travel straight across the harbor?

Answer 1

The kayaker must paddle at an angle west of north to counteract the eastward tidal current by using vector addition and trigonometry to calculate the exact angle.

Step-by-step explanation:

The student has asked how to paddle straight across a harbor with a tidal current moving east. The kayaker needs to compensate for the eastward tidal current while trying to move north. Given the current is 3 m/s to the east and the kayaker paddles at 4 m/s, the kayaker must paddle at an angle to the west of north to counteract the eastward movement. This can be solved using vector addition.

1. Label the vectors: let velocity of the kayak (Vkayak) be 4.0 m/s and velocity of the current (Vcurrent) be 3.0 m/s.
2. Draw a vector diagram with Vkayak pointing north and Vcurrent pointing east.
3. Calculate the angle (θ) to paddle west of north using trigonometry: tan(θ) = Vcurrent/Vkayak, so θ = tan-1(3/4).
4. Paddle at an angle of θ west of north to compensate for the current.

Once the angle is computed, the kayaker will know in which direction to paddle to reach directly across the harbor.