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Motion in a Plane

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Question : 25 of 32
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An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the speed of the aircraft?
Solution:  
Suppose that O is the observation point on the ground. The aircraft is flying along XY at a height OC = 3,400 m from the ground. Let A and B be two positions of the aircraft 10 s apart. Thus, the aircraft goes from the point A to C (or from the point C to B) in 5 s. If the angle subtended by AB is 30° at the point O, then the angle subtended by AC (distance covered in 5 s) at O is 15° From the right angled ΔOAC.
tan15=ACOC\tan 15^{\circ}= \frac{AC}{OC} or AC=OCtan15AC=OC \tan 15^{\circ} =3,400×0.2679=3{,}400 \times 0.2679 =910.86m=910.86\,\text{m}
Since the distance AC is covered by the aircraft in 5 s, the speed of the aircraft,
v=910.865=182.2ms1v= \frac{910.86}{5}=182.2\,\mathrm{m\,s^{-1}}
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