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anyanavicka [17]
3 years ago
10

Please Help! I'm stuck on this question. Show all work!

Mathematics
1 answer:
Valentin [98]3 years ago
6 0

Add all the displacement vectors together, then find the magnitude of this vector sum.

\vec r_1=(72\,\mathrm{km})(\cos60^\circ\,\vec\imath+\sin60^\circ\,\vec\jmath)

\vec r_2=(48\,\mathrm{km})(\cos270^\circ\,\vec\imath+\sin270^\circ\,\vec\jmath)

\vec r_3=(100\,\mathrm{km})(\cos150^\circ\,\vec\imath+\sin150^\circ\,vec\jmath)

Summing these vectors gives the resultant displacement

\vec r=\vec r_1+\vec r_2+\vec r_3\approx(-50.6\,\vec\imath+64.4\,\vec\jmath)\,\mathrm{km}

and we have

\|\vec r\|=\sqrt{(-50.6)^2+64.4^2}\,\mathrm{km}\approx\boxed{81.9\,\mathrm{km}}

so the plane ends up about 81.9 km away from its starting position.

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