Question

please answer this question with complete steps ​


The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 s, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 2500 m, then find the average speed of the aeroplane.

Answer 1

Answer:

Let E and D be the two positions of the plane and A be the point of observation.  

Let ABC be the horizontal line through A.

It is given that angles of elevation of the plane in two positions E and D are a point A are 60  

o

 and 30  

o

 respectively.

∠EAB=60  

o

, ∠DAB=30  

o

.  

It is also given that EB=3000  

3

​

 m.

In ΔABE,tan60  

o

=  

AB

BE

​

 

1

3

​

 

​

=  

AB

3000  

3

​

 

​

 

AB=3000 m

In ΔACD,tan30  

o

=  

AC

DC

​

 

3

​

 

1

​

=  

AC

3000  

3

​

 

​

 

AC=9000 m

Distance =BC=AC–AB=9000–3000=6000 m

The plane travels 6 km in 30 second,

Then the speed of the plane =  

30

6000

​

=200m/sec