Question

An aeroplane which was supposed to spray extinguish fires from an observation point was observed to be at an angle of elevation 45 degree. after 15 seconds the angl of elevation changes to 30 degree. if the aeroplane is flying at a height of 2500 metre and the extinguisher spray is spreading over a width of 100 metre , find the area covered by the spray in15 seconds?

Answer 1

The initial position of the plane is $x_i = 2500\cot (45^{\circ}) m = 2500 m$. The final position of the plane is $x_f = 2500\cot (30^{\circ}) m = 2500\sqrt 3 m$.
The plane has thus covered a length $x_f - x_i = 2500(\sqrt 3 - 1)m$.
Since it sprays over a width of 100m, we can say that the area covered by the spray is the length covered by the plane multiplied by the width sprayed over.

Hence the area is $100\times 2500(\sqrt 3 - 1) m^2$. You can calculate the rest.