An airplane is traveling 675 km/h in a direction 42.5° west of north
(a) Find the components of the velocity vector in the northerly and westerly directions.
b) How far north and how far west has the plane traveled after 3.00 h?
To find the components of the velocity vector in the northerly and westerly directions, you can use trigonometry.
(a) Components of the velocity vector:
The velocity vector has two components: the northerly component and the westerly component.
Given:
Speed of the airplane = 675 km/h
Direction = 42.5° west of north
To find the northerly component of the velocity vector, you can use the sine function:
northerly component = speed * sin(direction)
northerly component = 675 km/h * sin(42.5°)
To find the westerly component of the velocity vector, you can use the cosine function:
westerly component = speed * cos(direction)
westerly component = 675 km/h * cos(42.5°)
Now, let's calculate these components:
northerly component = 675 km/h * sin(42.5°)
= 675 km/h * 0.6703
≈ 453.476 km/h
westerly component = 675 km/h * cos(42.5°)
= 675 km/h * 0.7410
≈ 500.175 km/h
Therefore, the northerly component of the velocity vector is approximately 453.476 km/h, and the westerly component is approximately 500.175 km/h.
(b) To find how far north and how far west the plane has traveled after 3.00 hours, you can multiply the respective components by the duration of time traveled.
Distance traveled north = northerly component * time
= 453.476 km/h * 3.00 h
≈ 1360.43 km
Distance traveled west = westerly component * time
= 500.175 km/h * 3.00 h
≈ 1500.53 km
Therefore, the plane has traveled approximately 1360.43 km north and 1500.53 km west after 3.00 hours.