Question

The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current that has a velocity of 2.20 m/s in a direction 30.0º east of north relative to the Earth. It encounters a wind that has a velocity of 4.50 m/s in a direction of 50.0º south of west relative to the Earth. What is the velocity of the wind relative to the water?

The velocity of the wind relative to the water is approximately:
a) 3.26 m/s
b) 4.12 m/s
c) 5.08 m/s
d) 6.04 m/s

Answer 1

The velocity of the wind relative to the water can be found by subtracting the velocity of the ocean current from the velocity of the wind.

Step-by-step explanation:

The velocity of the wind relative to the water can be found by considering the velocity vectors of the ocean current and wind relative to the Earth. To find the velocity of the wind relative to the water, we need to subtract the velocity of the ocean current from the velocity of the wind.

The velocity of the ocean current is 2.20 m/s at an angle of 30.0° east of north. The velocity of the wind is 4.50 m/s at an angle of 50.0° south of west.

By subtracting these vectors, we can find the resultant velocity of the wind relative to the water. The magnitude of the resultant velocity is approximately 3.26 m/s, which means the correct answer is (a) 3.26 m/s.