The angle of elevation of an aero plane from a point on the ground is 45∘. After a flight of 15 seconds, the elevation changes to 30∘. If the aeroplane flying at a height of 3000 meters, find the speed of the aeroplane.

Given,Height of aero plane, AB=CD= 5000 mSuppose distance between two points BD=x mHorizontal distance from the point on ground to the final position of plane EB= y mIn ΔAEB we have,tan⁡45∘=ABEB 1=3000y y=3000 m ……. (i)Here, ED =BD+BEED=x+yNow, in ΔCED we have,tan⁡30∘=CDED13=3000x+y x+y=30003 ……. (ii)Put the value of y from equation (i),x+3000=30003 ⇒x=30003-3000 ⇒x=30003-1⇒x=30001.732-1⇒x=30000.732⇒x=2196 m Now we know that,Speed of Aero plane= Distance (x) Time taken s=219615m/sec s=146.4 m/sec s=219615×185km/hr. s=527.04 km/hr.So, speed of aero plane = 527.04 km/hr.Hence, option 3 is correct.

The angle of elevation of an aero plane from a point on the ground is 45∘. After a flight of 15 seconds, the elevation changes to 30∘. If the aeroplane flying at a height of 3000 meters, find the speed of the aeroplane.

Given,Height of aero plane, AB=CD= 5000 mSuppose distance between two points BD=x mHorizontal distance from the point on ground to the final position of plane EB= y mIn ΔAEB we have,tan⁡45∘=ABEB 1=3000y y=3000 m ……. (i)Here, ED =BD+BEED=x+yNow, in ΔCED we have,tan⁡30∘=CDED13=3000x+y x+y=30003 ……. (ii)Put the value of y from equation (i),x+3000=30003 ⇒x=30003-3000 ⇒x=30003-1⇒x=30001.732-1⇒x=30000.732⇒x=2196 m Now we know that,Speed of Aero plane= Distance (x) Time taken s=219615m/sec s=146.4 m/sec s=219615×185km/hr. s=527.04 km/hr.So, speed of aero plane = 527.04 km/hr.Hence, option 3 is correct.

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The angle of elevation of an aero plane from a point on the ground is $45^{\circ}$ . After a flight of 15 seconds, the elevation changes to $30^{\circ}$ . If the aeroplane flying at a height of 3000 meters, find the speed of the aeroplane.

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522.01 km/hr.

525.02 km/hr.

527.04 km/hr.

529.04 km/hr.

answer is C.

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Detailed Solution

Given,
Height of aero plane, AB=CD= 5000 m
Suppose distance between two points BD=x m
Horizontal distance from the point on ground to the final position of plane EB= y m
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