1) The north component of the airplane velocity is 260 km/h.
2) The direction of the plane is north of east.
Explanation:
1)
In this problem, we have to resolve the velocity vector into its components.
Taking east as positive x-direction and north as positive y-direction, the components of the velocity along the two directions are given by:
where
v is the magnitude of the velocity
is the angle between the direction of the velocity and the positive x-axis (the east direction)
For the airplane in this problem,
v = 750 km/h
So, the two components are
So, the component in the north direction is 256.5 km/h, so approximately 260 km/h.
2)
In this problem, we have to use vector addition.
In fact, the motion of the plane consists of two displacements:
- A first displacement of 220 km in the east direction
- A second displacement of 100 km in the north direction
Using the same convention of the same problem (x = east and y = north), we can write
Since the two vectors are perpendicular to each other, we can find their magnitude using Pythagorean's theorem:
And the direction is given by
north of east.
Learn more about vectors here:
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