The captain of a boat wants to travel directly across a river that flows due east with a speed of 1.09 m/s. He starts from the south bank of the river and wants to reach the north bank by travelling straight across the river. The boat has a speed of 6.44 m/s with respect to the water. What direction (in degrees) should the captain steer the boat? Note that 90° is east, 180° is south, 270° is west, and 360° is north.

Vbc = Vb + Vc = 6.44i

Vb + 1.09 = 6.44i
Vb = -1.09 + 6.44i

Tan Ar = Y/X = 6.44/-1.09 = -5.90826
Ar = -80.4o = Reference angle.
A = -80.4 + 180 = 99.6o, CCW = 9.6o W. of N.

346.5

To determine the direction the captain should steer the boat, we can use the concept of vector addition. The boat's velocity relative to the ground is the vector sum of its velocity relative to the water and the water's velocity.

1. Draw a diagram representing the situation. Label the horizontal direction as east and the vertical direction as north.

2. Represent the water's velocity as a vector pointing due east with a magnitude of 1.09 m/s. This vector will have a length to scale, but no vertical component since the river flows only horizontally.

3. Represent the boat's velocity relative to the water as a vector pointing in the unknown direction with a magnitude of 6.44 m/s. This vector will be longer than the water's velocity vector, as the boat is faster.

4. Connect the tail of the water's velocity vector to the head of the boat's velocity vector. The vector connecting these two points is the boat's velocity relative to the ground.

5. Measure the angle between this resultant vector and due east (i.e., the horizontal direction). This angle represents the direction the captain should steer the boat.

6. Use a protractor or any similar measuring device to measure the angle. Note that the angle is always measured counterclockwise from the reference direction (east).

7. Convert the measured angle to the appropriate format. If the angle is less than 90°, simply report the angle as the answer. If the angle is between 90° and 180°, subtract the angle from 180° to get the correct direction. If the angle is between 180° and 360°, subtract the angle from 360° to get the correct direction.

Note: The specific value of the angle will depend on the magnitudes of the given velocities, but the steps provided here will help you find the correct direction.

To determine the direction the captain should steer the boat, we need to consider the velocity of the boat relative to the ground. This velocity is the vector sum of the boat's velocity relative to the water and the velocity of the water.

We can represent the velocity of the boat relative to the water as a vector pointing east, with a magnitude of 6.44 m/s. The velocity of the water can be represented as a vector pointing due east, with a magnitude of 1.09 m/s.

To find the resultant velocity vector, we can use vector addition. Since both vectors are pointing in the same direction, we can simply add their magnitudes to get the magnitude of the resultant vector.

Magnitude of resultant velocity = magnitude of boat's velocity + magnitude of water's velocity
= 6.44 m/s + 1.09 m/s
= 7.53 m/s

The direction of the resultant velocity vector can be found using trigonometry. Since the boat's velocity vector is directed east (90°), and the water's velocity vector is directed east (also 90°), the angle between them is 0°. Therefore, the resultant velocity vector is also directed east, or 90°.

In conclusion, the captain should steer the boat at an angle of 90° (east) in order to travel directly across the river.