A kayaker needs to paddle north across a 100-m-wide harbor. The tide is going out, creating a tidal current that flows to the east at 2.0 m/s. The kayaker 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?

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

Explanation:

Using Pythagoras theorem, taking the direction it must go line as the hypotenuse

vh² = vs² + vd² vs is the speed of the stream, vh is the speed in the direction it must go to the vertical and vd is the speed going directly north

3 ² = 2² + vd²

9 - 4 = vd²

√5 = vd

2.24 m/s = vd which is the resultant speed

the direction it will go = tan θ = 2 / 2.24

θ = tan⁻¹(2 / 2.24) = 41.8° to the vertical ( west of North)

b)t = distance / v = 100 / 2.24 = 44.6 s