Let's do this question.
And Lighthouse sends out a beam of light extending from north, east to northwest.
A person on a ship sailing due east first sees the light when he's eight km away from the lighthouse.
He continues to see it, but 20 square root of two minutes.
What is the speed of the ship?
All right.
The video, give it a try and then let's do it together.
All right, we are back.
I hope you have given it a try.
Let's do it together now.
Let's mark the area covered by the beam of light.
OK, let's draw it over here.
Let this be the lighthouse and it extends its light from north east.
Right northeast is this direction to northwest, which is this direction over here.
So from here till here, it keeps rotating and it gives light.
Now, a person on a ship sailing due east but sees the night when is it a kilometer away from the lighthouse.
So the ship is over here.
And it's sailing due east, right, so it's moving in this direction and he sees the light when he's
eight kilometers away from the lighthouse that is this distance is eight km.
Right.
Now he sees the light for 20 square root of two minutes right now, let's draw the directions over here.
This is north to south, east and west.
Now, this angle over here is a 90 degree angle, right?
We have seen that before.
The angle between northwest and north east is equal to 90 degree.
Right, because north east bisects the angle between north and east.
But this angle will refortified.
This angle will be fortify.
Similarly, this and this is also forty five point forty five plus forty five gives you ninety degree.
That's why the angle between Northwest and northeast is equal to 90 degrees.
All right.
Now, over here you have eight kilometers here.
Also, you will have eight kilometers.
These two sides will be equal.
Let me mark these two points as P and Q.
Now we can see that BQ will be equal to square root of two into eight kilometers.
Why is that so?
Because you have eight and eight over here.
These are similar, right, of eight and eight over here.
So BQ Square.
Is equal to eight squared, plus eight squared, that's two in the eight squared, therefore BQ will
be rude to into eight kilometers.
All right, that's the length of.
Now, we know that speed is equal to distance by time.
Right.
That's why you say that she traveled at 20 kilometers per hour, kilometers distance, hours time.
So speed is distance by time.
Now, over here, we have the distance in kilometers and the time we have it in minutes.
And you can see that in the answer options, we have meter per second in each of the answer options.
So we need to convert kilometer to meter and minutes, two seconds and substitute it over here.
So distance in meters is eight, route two in 2000 and time in seconds is twenty two to sixty.
So this over here becomes eight through two in two thousand by twenty.
Two into sixty.
Right now let's cancel out the common factors from the numerator and denominator.
And we are left with eight in ten by two in the six which is the same as twenty by three meters per
second.
Right.
Because you can cancel out again common factors.
Therefore you have to by three and that's twenty by three meters per second.
And that is your answer.
Option B.