An aeroplane flying horizontally 1   km above the ground is observed at an elevation of 60 o and after 10 seconds the elevation is observed to be 30 o . The uniform speed of the aeroplane (in km / h ), is

Step-by-step solution

Let, d is the distance covered by aeroplane in 10 s e c . Let, the height at which the plane is flying be H = 1   km ⇒ H = A C = B D = 1   km In ∆ O A C , tan ⁡ 60 o = A C O C O C = 1 cot ⁡ 60 o ...(i) In ∆ O B D , tan ⁡ 30 o = B D O D O D = 1 cot ⁡ 30 o ...(ii) Now, d = A B = C D = O D - O C d = cot ⁡ 30 o - cot ⁡ 60 o S p e e d = d t = cot ⁡ 30 o - cot ⁡ 60 o 10 k m / s e c Speed in k m / h = cot ⁡ 30 o - cot ⁡ 60 o 10 ×