A plane, travelling with a velocity relative to the air of 320 km/h [28° S of W],
passes over Winnipeg. The wind velocity is 72 km/h [S]. Determine the displace-
ment of the plane from Winnipeg 2.0 h later.
To find the displacement of the plane from Winnipeg, we need to find the resultant velocity of the plane relative to the ground.
First, let's break down the given information into its components.
The velocity of the plane relative to the air is 320 km/h [28° S of W]. This means the plane is moving at a speed of 320 km/h and at an angle of 28° south of west.
The wind velocity is 72 km/h [S]. This means the wind is blowing at a speed of 72 km/h in the southern direction.
To find the resultant velocity, we can use vector addition.
Let's start by finding the component of the plane's velocity in the west direction.
The west component can be found using the formula: west component = velocity * cos(angle)
west component = 320 km/h * cos(28°)
= 320 km/h * cos(28°)
≈ 285.88 km/h to the west
Now, let's find the component of the plane's velocity in the south direction.
The south component can be found using the formula: south component = velocity * sin(angle)
south component = 320 km/h * sin(28°)
= 320 km/h * sin(28°)
≈ 147.01 km/h to the south
Now, let's find the resultant velocity by adding the components of the plane's velocity and the wind's velocity.
resultant velocity (west component) = 285.88 km/h + 0 km/h (since there is no west component of the wind's velocity)
= 285.88 km/h
resultant velocity (south component) = 147.01 km/h + (-72 km/h) (since the wind is blowing in the southern direction)
= 75.01 km/h
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity.
resultant velocity = √(west component^2 + south component^2)
resultant velocity = √(285.88^2 + 75.01^2)
≈ 299.26 km/h
The displacement of the plane from Winnipeg 2.0 hours later can be found by multiplying the resultant velocity by the time.
displacement = resultant velocity * time
= 299.26 km/h * 2.0 hrs
= 598.52 km
Therefore, the displacement of the plane from Winnipeg 2.0 hours later is approximately 598.52 km.