A passenger walks from one side of a ferry to the other as it approaches a dock. If the passenger's velocity is 1.50 m/s due north relative to the ferry, and 4.50 m/s at an angle of 30.0* west of north relative to the water, what are the direction and magnitude of the ferry's velocity relative to the water?
To find the direction and magnitude of the ferry's velocity relative to the water, we can use vector addition.
Given the passenger's velocity relative to the ferry as 1.50 m/s due north and 4.50 m/s at an angle of 30.0° west of north relative to the water, we need to add these two vectors.
1. Start by drawing a vector diagram. Draw a vertical line representing the north direction relative to the ferry. From the top of this line, draw a vector 1.50 units long upwards to represent the passenger's velocity relative to the ferry. Then, from the end of this vector, draw a second vector 4.50 units long at an angle of 30.0° west of north to represent the passenger's velocity relative to the water.
2. Now, draw a vector from the starting point to the end point of the second vector. This represents the ferry's velocity relative to the water.
3. Measure the magnitude of the ferry's velocity by measuring the length of the third vector.
4. Measure the direction of the ferry's velocity by using a protractor or angle measuring tool to find the angle between the third vector and the north direction. This angle represents the direction of the ferry's velocity relative to the water.
By following these steps, you should be able to determine the direction and magnitude of the ferry's velocity relative to the water.