Question

An aeroplane flying horizontally 1 km above the ground and going away from the observer is observed at an elevation of 60°. After 10 seconds, its elevation is observed to be 30°; find the uniform speed of the aeroplane in km per hour.

Answer 1

Let A be the aeroplane and B be the observer on the ground. The vertical height will be AC = 1 km = 1000 m. After 10 seconds, let the aeroplane be at point D.

Let the speed of the aeroplane be x m/sec.

∴ CE = 10x 

In ΔABC, 

`(AC)/(BC) = tan 60^circ`

`=> 1000/(BC) = sqrt(3)`

`=> BC = 1000/sqrt(3)m`

In ΔBDE, 

`(DE)/(BE) = tan 30^circ`

`=> BE = 1000 sqrt(3)`

∴ CE = BE – BC

`=> 10x = 1000sqrt(3) - 1000/sqrt(3)`

`=> x = 100 (sqrt(3) - 1/sqrt(3))`

= 100 × 1.154

= 115.4 m/sec

= `115.4 xx 18/5` km/hr

= 415.44 km/hr

Hence, speed of the aeroplane is 415.44 km/hr.