An aeroplane flying horizontally 1000m above the ground is observed at an angle of elevation 600 froma point on the - Maths - Some Applications of Trigonometry

Question

An aeroplane flying horizontally 1000m above the ground is
observed at an angle of elevation 600 froma point on the
ground Aftera flight of 10secondsthe angle of elevation at a point
of observation changes to 300 Find the speed of the
plane in m/s

Vimala · Accepted Answer

Let us observe the following figure

Let A and B be the two positions of the aeroplane and let O be the point of observation $∠ C O A = 60^{\circ}, ∠ D O B = 30^{\circ}$ and AC = BD = 1000 m From the right triangle OCA, we have $\frac{O C}{A C} = \cot 60^{\circ} = \frac{1}{\sqrt{3}} \frac{O C}{1000} = \frac{1}{\sqrt{3}} O C = \frac{1000}{\sqrt{3}} m$ From the right triangle ODB, we have $\frac{O D}{B D} = \cot 30^{\circ} = \sqrt{3} \frac{O D}{1000} = \sqrt{3} O D = 1000 \sqrt{3} m$ $C D = O D - O C = 1000 \sqrt{3} - \frac{1000}{\sqrt{3}} = 1000 (\sqrt{3} - \frac{1}{\sqrt{3}}) = 1000 \times \frac{2}{\sqrt{3}} = \frac{2000}{\sqrt{3}} m \approx 1154 700 m$ We need to find the speed of the plane $S p e e d = \frac{D i s \tan c e}{T i m e} = \frac{1154 7 m}{10 \sec o n d s} = 115 47 m / s$ Thus the speed of the plane is 115 47 m /s

An aeroplane flying horizontally 1000m above the ground is observed at an angle of elevation 600 froma point on the ground.Aftera flight of 10secondsthe angle of elevation at a point of observation changes to 300 .Find the speed of the plane in m/s.

An aeroplane flying horizontally 1000m above the ground is observed at an angle of elevation 60⁰ froma point on the ground.Aftera flight of 10secondsthe angle of elevation at a point of observation changes to 30⁰ .Find the speed of the plane in m/s.