Question

an aircraft is flying at the height of 3600 m from the ground if the angle subtended at the ground observation point by aircraft position 10 seconds apart 30 degree the speed of aircraft is?
a) 600π
b)60π
c)120π
d)3600π

Answer 1

Answer is 120√3 m/s . $\pi$ has nothing to do here

Imagine a triangle formed from 3 vertices where 1 vertice is the person standing on ground, second vertice is the position of plane in the beginning and third vertice is the position of the plane after 10 seconds. the triangle formed is right angled at the initial plane position.

Now, tan 30 = distance travelled by plane / distance of plane from ground

Thus 1/√3 = D / 3600 --- > D = 3600/√3 OR 1200√3

Now speed is simply = D/Time

= 1200√3 ÷ 10

= 120√3 m/s