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Let's do this question.

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And Lighthouse sends out a beam of light extending from north, east to northwest.

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A person on a ship sailing due east first sees the light when he's eight km away from the lighthouse.

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He continues to see it, but 20 square root of two minutes.

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What is the speed of the ship?

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All right.

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The video, give it a try and then let's do it together.

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All right, we are back.

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I hope you have given it a try.

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Let's do it together now.

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Let's mark the area covered by the beam of light.

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OK, let's draw it over here.

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Let this be the lighthouse and it extends its light from north east.

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Right northeast is this direction to northwest, which is this direction over here.

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So from here till here, it keeps rotating and it gives light.

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Now, a person on a ship sailing due east but sees the night when is it a kilometer away from the lighthouse.

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So the ship is over here.

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And it's sailing due east, right, so it's moving in this direction and he sees the light when he's

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eight kilometers away from the lighthouse that is this distance is eight km.

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Right.

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Now he sees the light for 20 square root of two minutes right now, let's draw the directions over here.

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This is north to south, east and west.

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Now, this angle over here is a 90 degree angle, right?

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We have seen that before.

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The angle between northwest and north east is equal to 90 degree.

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Right, because north east bisects the angle between north and east.

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But this angle will refortified.

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This angle will be fortify.

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Similarly, this and this is also forty five point forty five plus forty five gives you ninety degree.

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That's why the angle between Northwest and northeast is equal to 90 degrees.

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All right.

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Now, over here you have eight kilometers here.

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Also, you will have eight kilometers.

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These two sides will be equal.

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Let me mark these two points as P and Q.

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Now we can see that BQ will be equal to square root of two into eight kilometers.

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Why is that so?

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Because you have eight and eight over here.

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These are similar, right, of eight and eight over here.

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So BQ Square.

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Is equal to eight squared, plus eight squared, that's two in the eight squared, therefore BQ will

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be rude to into eight kilometers.

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All right, that's the length of.

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Now, we know that speed is equal to distance by time.

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Right.

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That's why you say that she traveled at 20 kilometers per hour, kilometers distance, hours time.

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So speed is distance by time.

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Now, over here, we have the distance in kilometers and the time we have it in minutes.

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And you can see that in the answer options, we have meter per second in each of the answer options.

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So we need to convert kilometer to meter and minutes, two seconds and substitute it over here.

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So distance in meters is eight, route two in 2000 and time in seconds is twenty two to sixty.

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So this over here becomes eight through two in two thousand by twenty.

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Two into sixty.

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Right now let's cancel out the common factors from the numerator and denominator.

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And we are left with eight in ten by two in the six which is the same as twenty by three meters per

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second.

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Right.

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Because you can cancel out again common factors.

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Therefore you have to by three and that's twenty by three meters per second.

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And that is your answer.

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Option B.