Final answer:
To find the velocity of the ship relative to the Earth, we need to combine its velocity relative to the water with the velocity of the ocean current relative to the Earth. By breaking down the velocities into their x and y components, we can calculate the ship's velocity relative to the Earth. The magnitude and direction of the ship's velocity can then be determined using the Pythagorean theorem and inverse tangent function.
Step-by-step explanation:
The velocity of the ship relative to the Earth can be found by combining the velocity of the ship relative to the water and the velocity of the ocean current relative to the Earth. We can break down the velocities into their x and y components.
The velocity of the ship relative to the Earth in the x-direction is the sum of the x-components of the ship's velocity relative to the water and the ocean current's velocity. In this case, the x-component of the ship's velocity relative to the water is 7.00 m/s and the x-component of the ocean current's velocity is 1.50 m/s * cos(40.0°). Adding these values gives us the x-component of the ship's velocity relative to the Earth.
The velocity of the ship relative to the Earth in the y-direction is the sum of the y-components of the ship's velocity relative to the water and the ocean current's velocity. In this case, the y-component of the ship's velocity relative to the water is 0 m/s (because the ship is moving north) and the y-component of the ocean current's velocity is 1.50 m/s * sin(40.0°). Adding these values gives us the y-component of the ship's velocity relative to the Earth.
Using these two components, we can calculate the magnitude and direction of the ship's velocity relative to the Earth using the Pythagorean theorem and inverse tangent function, respectively.