Question

. A plane leaves the airport in
Galisteo and flies 170 km at 68° east of north and then changes
direction to fly 230 km at 48° south of east, after which it makes
an immediate emergency landing in a pasture. When the airport
sends out a rescue crew, in which direction and how far should this
crew fly to go directly to this plane?
​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

The rescue crew will have to travel 329.46km, towards 18.99° south of east.

Explanation:

We just need to add the vectors of the different path that the plane took. We can use the component method, where descompose each vector in their x and y component and add the corresponding components:

Path 1:

Here, you need to keep in mind that the angle given is from the y-axis (north)

Path 2:

The angle is from the x-axis, but the vertical distance is toward south:

Summation:

As the y-component is negative, and the x-component positive, the rescue crew will have to move towards south of east.

Now, we use Pythagoras and trygonometry to find the magnitude and direction of the resulting vector:

18.99° south of east.