Final answer:
The resultant velocity of the boat as measured from the land is approximately 22.18 meters/second in the direction of 81.35 degrees north of east.
Step-by-step explanation:
In order to find the resultant velocity of the boat as measured from the land, we need to calculate the vector sum of the boat's velocity with respect to the water and the river's velocity. The boat's velocity is given as 22 meters/second north, and the river's velocity is given as 2 sqrt(2) meters/second east.
To find the resultant velocity, we can use the Pythagorean theorem to calculate the magnitude and trigonometry to find the direction.
The magnitude of the resultant velocity is found using the formula sqrt((V_boat)^2 + (V_river)^2), where V_boat is the boat's velocity and V_river is the river's velocity. Plugging in the given values, we get sqrt((22^2) + (2 sqrt(2))^2) = sqrt(484 + 8) = sqrt(492) = 22.18 meters/second (approximately).
The direction of the resultant velocity can be found using the tangent function. The tangent of the angle between the resultant velocity and the x-axis is given by tan(theta) = V_boat / V_river. Plugging in the given values, we get tan(theta) = 22 / (2 sqrt(2)) = 22 / (2 * 1.414) = 7.77. Taking the arctan of this value, we find theta = 81.35 degrees.
Therefore, the resultant velocity of the boat as measured from the land is approximately 22.18 meters/second in the direction of 81.35 degrees north of east.