a plane is flying at an altitude of 2 km the elevation is 30 degree after exactly 1 - Maths - Some Applications of Trigonometry

Question

a plane is flying at an altitude of 2 km the elevation is 30
degree after exactly 1 minute it is at an angle of elevation 60
degree maintaining the same altitude the speed of the plane is

Gursheen kaur. · Accepted Answer

Given , h = 2km =2000m
Let A be the base of plane. The plane is at point D in first and at point E at the second sweep.

DE = total distance it covers in 1 min.

now, from the figure,

In tr. DAC,

tan 30° = Perp/ base

tan30° = DC/AC = h/AC

and In tr. EAB,

tan 60° = EB/AB = h/AB

as, it is given that, distance covered by plane in 1 min. , DE=AC-AB

$D E = \frac{h}{\tan 30^{0}} - \frac{h}{\tan 60^{0}} = \frac{2000}{\frac{1}{\sqrt{3}}} - \frac{2000}{\sqrt{3}} D E = 2000 \sqrt{3} - \frac{2000}{\sqrt{3}} = \frac{6000 - 2000}{\sqrt{3}} = \frac{4000}{\sqrt{3}} = \frac{4000}{3} \sqrt{3} = 2309.40 m$

thus, the velocity of plane , V = dist. covered/ time taken = DE/ 60 [1min = 60 sec]

V= 2309.40/60 = 38.49m/s

a plane is flying at an altitude of 2 km. the elevation is 30 degree. after exactly 1 minute it is at an angle of elevation 60 degree maintaining the same altitude. the speed of the plane is