Final answer:
To calculate the velocity of the boat as viewed by an observer on the shore, combine the velocity of the river and the velocity of the boat relative to the water using Pythagorean theorem. The resultant velocity is approximately 10.893 m/s at an angle of 82.63° north of east.
Step-by-step explanation:
Calculating the Velocity of a Boat Relative to the Shore
When considering the motion of a boat crossing a river with a given current, we need to take into account two velocities: the velocity of the boat relative to the water, and the velocity of the river itself. The student's question involves a boat that moves due north with respect to the water, and a river that flows due east. To find the velocity of the boat as viewed by an observer on the shore, we combine these two velocity vectors.
The velocity of the river is 1.41 m/s due east, and the velocity of the boat relative to the water is 10.8 m/s due north. Using vector addition, we can calculate the resultant velocity of the boat relative to an observer on the shore.
Since these two velocities are perpendicular to each other, we use Pythagorean theorem to determine the magnitude of the resultant velocity:
Plugging in the values:
To find the direction of the resultant velocity, we can use the inverse tangent function (tan-1):
Therefore, the velocity of the boat as viewed by an observer on the shore is approximately 10.893 m/s at an angle of 82.63° north of east.