Question

from the top of a light house the angle of depression of a ship sailing towards it was found to be 30 o .after 10 seconds the angle of depression changes to 60 o .assuring that the ship is sailing at uniform speed,find how much time it will take to reach the light house.

Answer 1

time will be 5 seconds
please see the attachment.

Answer 2

Answer:

It will take 5 seconds to reach from point C and total time from Point D is 15 seconds

Step-by-step explanation:

Let H be the height of lighthouse

The angle of depression of the ship changes from 30 to 60 in 10 sec

In ΔABD

$tan \theta = \frac{perpendicular}{Base}$

$tan30^{\circ} = \frac{AB}{BD}$

$\frac{1}{\sqrt{3}} = \frac{H}{BD}$

$BD= \frac{H}{\frac{1}{\sqrt{3}} }$

In ΔABC

$tan \theta = \frac{perpendicular}{Base}$

$tan60^{\circ} = \frac{AB}{BC}$

$\sqrt{3}= \frac{H}{BC}$

$BC= \frac{H}{\sqrt{3}}$

Now distance traveled in 10 minutes = BD -BC =$\frac{H}{\frac{1}{\sqrt{3}} }- \frac{H}{\sqrt{3}}=\frac{2H}{\sqrt{3}}$

$Speed = \frac{Distance}{Time}$

$Speed = \frac{\frac{2H}{\sqrt{3}}}{10}$

If the ship reaches the light house the distance becomes 0 from $\frac{H}{\sqrt{3}}$

So, $Time = \frac{Distance}{Speed}$

$Time = \frac{\frac{H}{\sqrt{3}}}{ \frac{\frac{2H}{\sqrt{3}}}{10}}$

$Time = 5$

So, It will take 5 seconds to reach from point C and total time from Point D = 10+5 =15 seconds