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?
now let the aircraft be initially at a point A situated 3400m above the ground, it moves with a speed v along straight line parallel to ground and reach a point B, now let us assume a recording station is located on ground at c which is in line with midway of the journey D
Suppose the plane covered a distance S and subtended an angle of 30o on recording station as it moved from A to B
The situation has been shown in the figure
We have to find speed of the plane; the plane is moving with constant speed so we will use the relation
S = v × t or v = S/t
Where S is the distance covered by plane moving with a speed v in time t
Here we are given time t = 10.0 s
So we need to find distance covered by plane S
Now we can see distance covered = AB = AD + BD
Since D is the midpoint of AB
AD = BD or distance AB = 2 × AD
Now in Triangle ACD using trigonometry we will find AD
now
Assuming D is the midpoint of AB and C is equidistant from A and B we have
Or
AD = CD × tan15o
CD = 3400m
tan15o= 0.2679
so we get
AD = 3400m × 0.2679
= 910.86m
So total distance covered by the plane
S = AB = 2 × 910.86m = 182.17m
So the Value of S = 182.17m and t = 10 s in the equation
v = s/t ,we get
speed of the plane
so plane is flying at a speed of 18.2 m/s