Question

A man on cliff Observes a boat, at an angle of depression 30°, Which is sailing towards the shores to the point Immediately underneath him. Three minutes later, the angle of depression of the boat is found to be 60°. Assuming that the Boat sails at a uniform speed, determine :
(i)How muchMore time it will take to reach the shore
(ii) The speed of the boat in metre per second, if height of the cliff is 500 m

Answer 1

Answer:

Step-by-step explanation:

Let height of cliff= AB=h

∠EAD=∠ADB (alternate interior ∠)

             =30  

o

                          (Refer to Image)

Also, ∠EAC=∠ACB=60  

o

 

Let speed of boat= V m/s

A/Q, DC=3×60V=180V

Let, BC=x

Time taken from C to B=t

⇒x=vt

Now, in △  

le

ABD,tan30  

o

=  

180v+vt

h

​  

 

⇒1  

3

​  

=  

180v+vt

h

​  

 

In △  

le

ABC, tan60  

o

=  

vt

h

​  

 

⇒  

3

​  

=  

vt

h

​  

 

⇒h=  

3

​  

vt

⇒  

3

​  

 

1

​  

=  

180v+vt

3

​  

vt

​  

 

⇒180+t=3t

⇒180=2t⇒t=90s= 1min30sec