Question

A ship sets sail from Rotterdam, The Netherlands, heading due north at 7.00 m/s relative to the water. The local ocean current is 1.50 m/s in a direction 40.0º north of east. What is the velocity of the ship relative to the Earth?

The velocity of the ship relative to the Earth is approximately:
a) 5.91 m/s
b) 6.72 m/s
c) 7.53 m/s
d) 8.34 m/s

Answer 1

The velocity of the ship relative to the Earth is approximately 8.145 m/s.

Step-by-step explanation:

To find the velocity of the ship relative to the Earth, we need to combine the ship's velocity relative to the water and the velocity of the ocean current.

First, we break down the velocity of the ocean current into its north and east components:

North component = 1.50 m/s * sin(40°) ≈ 0.962 m/s

East component = 1.50 m/s * cos(40°) ≈ 1.145 m/s

Next, we add the ship's velocity relative to the water and the ocean current's east component:

Velocity relative to Earth = 7.00 m/s + 1.145 m/s ≈ 8.145 m/s

Therefore, the velocity of the ship relative to the Earth is approximately 8.145 m/s.