To find the velocity of the boat relative to the shore, we can use vector addition.
Let's consider the boat's velocity as it moves across the river and the velocity of the river's flow.
The boat's velocity relative to the shore consists of two components:
- The boat's velocity relative to the water (across the river).
- The velocity of the river's flow.
Given:
- Boat's velocity across the river: 3.5 m/s (northward)
- River's flow velocity: 1.7 m/s (eastward)
Since the velocities are perpendicular to each other, we can use the Pythagorean theorem to find the resultant velocity.
The magnitude of the resultant velocity can be calculated as follows: Resultant velocity = √((velocity across the river)^2 + (velocity of river's flow)^2)
Plugging in the values: Resultant velocity = √((3.5 m/s)^2 + (1.7 m/s)^2)
Calculating the square of each term: Resultant velocity = √(12.25 m^2/s^2 + 2.89 m^2/s^2) Resultant velocity = √15.14 m^2/s^2
Taking the square root: Resultant velocity ≈ 3.89 m/s
The direction of the resultant velocity can be determined using trigonometry. Since the boat is moving northward (upward) and the river's flow is eastward (to the right), the resultant velocity will be at an angle between north and east.
Using trigonometry: tan(theta) = (velocity of the river's flow)/(velocity across the river) tan(theta) = 1.7 m/s / 3.5 m/s theta ≈ 26.6 degrees
Therefore, the velocity of the boat relative to the shore is approximately 3.89 m/s in a direction approximately 26.6 degrees north of east.