Question

A plain leaves the airport in Galisteo and flies 170 km at the north and then changes direction to fly 250 km at of east, after which it makes an immediate emergency landing in a pasture. When the airports sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?

Answer 1

Answer on Question#56441 - Physics - Field Theory

A plain leaves the airport in Galisteo and flies $a = 170 \, \text{km}$ at the north and then changes direction to fly $b = 250 \, \text{km}$ at of east, after which it makes an immediate emergency landing in a pasture. When the airports sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?

Solution:

The distance from the airport is

$$c = \sqrt {a ^ {2} + b ^ {2}} = \sqrt {(1 7 0 \mathrm {k m}) ^ {2} + (2 5 0 \mathrm {k m}) ^ {2}} = 3 0 2 \mathrm {k m}$$

The angle $\theta$ is

$$\theta = \mathrm {a t a n} \frac {b}{a} = \mathrm {a t a n} \frac {2 5}{1 7} = 5 5. 7 8 {}^ {\circ}$$

Answer: distance - 302 km, $\theta = 55.78{}^{\circ}$

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