An aeroplane flying at a constant speed, parallel to the horizontal ground, 3 km above it is observed at an elevation of 60 ° from a point on the ground. If after five seconds, its elevation from the same point is 30 ° , then the speed (in km / hr ) of the aeroplane is

Step-by-step solution

Let from point C the angle of elevation of plane at B is 60 ° . and after 5 seconds it reach at B ' In ∆ A B C ,   A C = 3 cot 60 ° = 1 In Δ C A ' B ' ,   A ' C = 3   cot 30 ° = 3 Hence, distance A A ' = A ' C - A C = 3 - 1 = 2 Now, speed equals total distance travelled divided by total time taken. Thus, speed = 2 5 60 × 60 = 2 × 60 × 60 5 = 7200 5 = 1440   km / hr