Motion in a Plane

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Question : 25
Total: 32
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°=
AC
OC
or AC=OCtan15° =3,400×0.2679 =910.86m
Since the distance AC is covered by the aircraft in 5 s, the speed of the aircraft,
v=
910.86
5
=182.2ms1
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