Question

A private plane travels from the city of Sheffield, UK, to the city of Nijmegen, The Netherlands.
a) In total, the plane travels 171.32km south and 495.20km east. What is the direct distance between Sheffield and Nijmegen?
b) Immediately after leaving the airport in Sheffield, the plane due north for 5km. It then made a turning of 48° towards the east and travelled for a further 5km.
At this point, how far was the plane from the airport in Sheffield?

Answer 1

Answer:

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Answer 2

(a) The direct distance between Sheffield and Nijmegen is 524 km

(b) At this point, the plane from the airport in Sheffield is at 9.13 km

Explanation:

The plane travels 171.32 km South and 495.20 km East

Thus, direct distance between Sheffield and Nijmegen

$=\sqrt{171.32^2+495.20^2}$

$=\sqrt{29350.54+245223.04}$

$=\sqrt{274573.58}$

$=524$ km

(b) The distance will be given by

$d=\sqrt{5^2+5^2+2\times 5\times 5\times \cos 48^\circ}$

$\implies d=\sqrt{50+50\times 0.669}$

$\implies d=\sqrt{83.456}$

$\implies d=9.13$ km

Hope this answer is helpful.

Know More:

Q: A body a travels a distance of 3km towards East, then 4km towards North and finally 9 km towards East. a) What is the total distance travelled b) What is the resultant displacement?

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