Final answer:
The resultant speed (magnitude of velocity) for the boat relative to the shore is approximately 8.06 meters/second.
Step-by-step explanation:
To find the resultant speed (magnitude of velocity) for the boat relative to the shore, we need to consider the velocities of the boat and the current separately. The boat has a velocity of 4 meters/second to the east relative to the water, while the current has a velocity of 7.0 meters/second to the north relative to the shore. To find the resultant velocity, we can use the Pythagorean theorem:
Resultant velocity = √(velocity of boat)^2 + (velocity of current)^2
Plugging in the values, we get:
Resultant velocity = √(4^2 + 7.0^2) = √(16 + 49) = √65 ≈ 8.06 meters/second