A person on a cruise ship is doing laps on the promenade deck. On one portion of the track the person is moving north with a speed of 3.6 m/s relative to the ship. The ship moves east with a speed of 12 m/s relative to the water.
To solve this problem, we need to break it down into separate components and consider the relative motion between the person and the water.
Let's define our coordinate system with the positive x-axis pointing east and the positive y-axis pointing north. The person's velocity relative to the ship is given as 3.6 m/s north.
Now let's consider the ship's velocity relative to the water. The ship is moving east with a speed of 12 m/s.
To find the person's velocity relative to the water, we need to add the two velocities together using vector addition. Since the velocities are given in terms of magnitudes and directions, we can represent them as vectors.
First, we convert the person's velocity (3.6 m/s north) into a vector form. Since it's moving directly north, the vector is (0, 3.6) m/s.
Next, we convert the ship's velocity (12 m/s east) into a vector form. Since it's moving directly east, the vector is (12, 0) m/s.
Now, we can add the two vectors together to get the person's velocity relative to the water.
(0, 3.6) m/s + (12, 0) m/s = (12, 3.6) m/s
Therefore, the person's velocity relative to the water is (12, 3.6) m/s, which means the person is moving northeast with a speed of approximately 12.17 m/s.
Note: In this problem, we assumed that the person's motion relative to the ship is not affected by any additional factors like wind or ocean currents. We only considered the motion of the ship relative to the water and the motion of the person relative to the ship.