the angle of an aeroplane friom a point on the ground is 45 degree After flight for 15 - Maths - Some Applications of Trigonometry

Question

the angle of an aeroplane friom a point on the ground is 45
degree After flight for 15 sec the elevation changess to 30 degree
If the aeroplane is flying at the heighht odf 3000 m Find the speed
of the aeroplane ?

Mayank Bhardwaj · Accepted Answer

Let the initial and final position of the plane be A and B Let O be the point of observation

AAÂ´ and BBÂ´ denote the height of the plane from the ground âˆ´ AAÂ´ = BBÂ´ = 3000 m From âˆ†OAAÂ´ $\tan 45 ° = \frac{A A^{'}}{{O A}^{'}} \Rightarrow {O A}^{'} = \frac{A A^{'}}{\tan 45 °} \Rightarrow {O A}^{'} = \frac{3000}{1} \Rightarrow {O A}^{'} = 3000 m$ From âˆ†OBBÂ´ $\tan 30 ° = \frac{B B^{'}}{{O B}^{'}} \Rightarrow {O B}^{'} = \frac{B B^{'}}{\tan 30 °} \Rightarrow {O B}^{'} = \frac{3000}{(\frac{1}{\sqrt{3}})} \Rightarrow {O B}^{'} = 3000 \sqrt{3} m$ Distance covered by the plane from A to B is AB or AÂ´BÂ´ â‡’ AÂ´BÂ´ = OBÂ´ â€“ OAÂ´ $= (3000 \sqrt{3} - 3000) m = 3000 (\sqrt{3} - 1) m = 3000 (1 73 - 1) m = (3000 \times 0 73) m = 2190 m$ Time taken by the plane in moving from A to B = 15 seconds Speed of the plane $= \frac{2190}{15} m / \sec$ = 146 m/sec

the angle of an aeroplane friom a point on the ground is 45 degree. After flight for 15 sec. the elevation changess to 30 degree. If the aeroplane is flying at the heighht odf 3000 m .Find the speed of the aeroplane ?