An oil spill on the ocean is sometimes modeled as having a velocity that has two components: a wind induced velocity that is 3% of the true wind velocity and an independent tidal velocity Vtidal. The tidal velocity is 3.0 km/hr due north and V wind = 40 km/hr 20 degrees north of east. In six hours, how far is the oil predicted to move in the northerly direction?

V = 3km/h[90o] + 40km/h[20o]

Y = 3 + 40*sin20 = 16.7km/h = Vertical
or Northerly component.

d = r*t = 16.7km/h * 6h = 100.1 km.

To find out how far the oil is predicted to move in the northerly direction, we need to determine the total velocity of the oil spill.

First, let's calculate the wind-induced velocity. We know that the wind-induced velocity is 3% of the true wind velocity.

Given:
Vwind = 40 km/hr (velocity of the wind, 20 degrees north of east)

To find the wind-induced velocity, we multiply the wind velocity by 3%:
Wind-induced velocity = (3/100) * Vwind

Wind-induced velocity = (3/100) * 40 km/hr

Wind-induced velocity = 1.2 km/hr (approx)

Next, let's calculate the total velocity of the oil spill by considering the wind-induced velocity and the tidal velocity.

Given:
Vtidal = 3.0 km/hr (velocity of tidal current in the north direction)

The total velocity of the oil spill is the vector sum of the wind-induced velocity and the tidal velocity.

To perform vector addition, we need to break down the velocities into their north and east components, since the tidal velocity is only given in the north direction.

For the wind-induced velocity, we know that it is 20 degrees north of east. We can use trigonometry to find its north and east components.

North component of wind-induced velocity = Wind-induced velocity * sin(20 degrees)
East component of wind-induced velocity = Wind-induced velocity * cos(20 degrees)

North component of wind-induced velocity = 1.2 km/hr * sin(20 degrees)
North component of wind-induced velocity ≈ 0.417 km/hr

The tidal velocity is already in the north direction, so its north component is simply Vtidal.

North component of total velocity = North component of wind-induced velocity + North component of tidal velocity

North component of total velocity = 0.417 km/hr + 3.0 km/hr

North component of total velocity ≈ 3.417 km/hr

Now, to find how far the oil is predicted to move in the northerly direction in six hours, we multiply the north component of total velocity by the time (6 hours):

Distance in the northerly direction = North component of total velocity * time
Distance in the northerly direction ≈ 3.417 km/hr * 6 hours

Distance in the northerly direction ≈ 20.502 km (approx)

Therefore, the oil spill is predicted to move approximately 20.502 km in the northerly direction in six hours.