Final answer:
The resultant velocity of the boat with respect to the shore is 5.83 m/s, which is calculated using the Pythagorean theorem due to the perpendicular vectors of the boat's motion and the river's current.
Step-by-step explanation:
The question is asking for the resultant velocity of a boat with respect to the shore, taking into account the boat's velocity and the river's current. When dealing with these types of problems in physics, we use vector addition to find the resultant vector.
In this scenario, the boat travels north at 3.0 m/s and the stream flows west at 5.0 m/s. These two vectors are perpendicular to each other, so to find the magnitude of the resultant velocity, we use the Pythagorean theorem:
Vtotal = √(Vboat2 + Vriver2)
Substituting the given values, we get:
Vtotal = √((3.0 m/s)2 + (5.0 m/s)2)
Vtotal = √(9 + 25)
Vtotal = √34
Vtotal = 5.83 m/s
The boat's resultant velocity with respect to the shore is 5.83 m/s at an angle to the north. To calculate the direction, we can use trigonometry (the arctangent function), but the question only asks for the magnitude of the velocity.