Final answer:
The resultant velocity of the kayaker is approximately 3.6 m/s, calculated using the Pythagorean theorem. The provided multiple-choice answers do not correctly correspond to this value, with the closest being numerically option 4) 4.0 m/s to the north, which is still inaccurate.
Step-by-step explanation:
To determine the resultant velocity of the kayaker, we should consider both the kayaker's paddling speed and the speed of the tidal current. Since the kayaker paddles north at a speed of 3.0 m/s and the tidal current flows east at 2.0 m/s, these two velocities are perpendicular to each other.
We can find the resultant velocity by using the Pythagorean theorem, since the motion of the kayaker and the current are at right angles to each other. The formula for the resultant velocity (Vr) is:
Vr = √((Vnorth)^2 + (Veast)^2)
Where Vnorth is the kayaker's velocity to the north, and Veast is the current's velocity to the east.
Vr = √((3.0 m/s)^2 + (2.0 m/s)^2) = √(9 + 4) = √13
Vr ≈ 3.6 m/s
The resultant velocity of the kayaker is therefore approximately 3.6 m/s, which is not directly north due to the eastward current.
However, it's crucial to note that none of the answer choices provided in the question correctly corresponds to this calculated resultant velocity. Thus, we should advise the student that the actual resultant velocity does not match any of the given options, and the closest option numerically would be option 4) 4.0 m/s to the north, even though it is mathematically inaccurate.