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Speed of a boat is measured
Transcript
00:00Unit 6, Trigonometry and Bearing, exercise 6.5, the last question, question no.10
00:06A boat moving away from a lighthouse 2.6.6 m high, take 120 seconds to change the angle of elevation of top of lighthouse from 60° to 45° point speed of boat.
00:20I have made some statements to save the time.
00:25We have the height of the lighthouse.
00:28The angle of elevation has changed from 60° to 45°.
00:33The time taken is 120 seconds.
00:36We have to find the speed of the boat.
00:41First of all, we will make the figure.
00:44You have the height.
00:46The height of the lighthouse is always a straight line.
00:50You will take a straight line.
00:52That is going to be the height.
00:59Now you have two angles of elevation.
01:03One is 60°.
01:07The higher the angle, the closer it will be to the point of observation.
01:14So this is going to be 60°.
01:1945° will come after this.
01:21It will be a little far.
01:29Now you can label it.
01:31You can take it as O, A, B, and C.
01:38Now what we have to find is the speed.
01:42But for that, we have to solve everything first.
01:46Here you will get the height of the tower.
01:49Now you will see that basically you are having two triangles.
01:52Whenever two lines are perpendicular, the angle will be 90°.
01:57One is OCA, the larger triangle.
02:01And the other is OBA.
02:04Which triangle will we solve first?
02:06We will solve OCA first.
02:08You take the triangle OCA.
02:16There are two triangles.
02:19You have to solve them separately.
02:21So that the question is solved very easily.
02:25You are having a triangle.
02:27That is OCA.
02:32And after that we will solve a triangle.
02:34The smaller one is OBA.
02:41Now you see, which trigonometric tissue will you apply on it?
02:46You will apply 10.
02:47Why?
02:48Because you have perpendicular in 10.
02:52And we have to involve the base.
02:54So, 10, 45°.
02:58You have O and A perpendicular.
03:02That is 206.6 m.
03:06And you will have all these bases.
03:09You can write AC or CA.
03:1210, 45° is equal to 1.
03:16So, it is going to be equal to 1, 206.6 AC.
03:22When AC is multiplied by 1, you will get AC again.
03:26So, basically you have all the bases here.
03:30That is 206.6 m.
03:33Now we come to our second triangle.
03:37You see, you have perpendicular, angle and again we have to involve the base.
03:44So, definitely we are going to use 10.
03:4710, 60°.
03:51Perpendicular, 206.6.
03:55And base is AB or BA.
03:5810, 60° is equal to √3.
04:02If you want, you can write it in decimals.
04:09We will do cross multiplication.
04:14I will put 1 below it.
04:16Now 1 will be multiplied by this.
04:18And I want to use decimal value of √3.
04:21It will be multiplied by this.
04:23So, AB will come here.
04:26But when 1 will be multiplied by 206, it will be like this.
04:33Now I want AB to shift here and √3 to come down.
04:38If AB goes up, we can switch it.
04:41And √3 comes down because I want to know AB.
04:45If you want to know, you have to isolate it.
04:48So, when we will divide it by 1.73, we will get value of AB.
04:55119.42 m.
04:59You see your figure, first you got value of CA.
05:04Now you got value of AB.
05:08If I subtract value of AB from value of CA, I will get value of CB.
05:25When I am subtracting these two values, I am getting value of 87.17 m.
05:37Now you wanted to know speed of the board.
05:41What is speed formula?
05:43We will write speed formula on this side.
05:46Speed is distance divided by time.
05:53Now you see, what is distance?
05:56It is 87.17 m.
05:58Time of point C and B is 120 seconds.
06:03120 seconds for change from point C to point B in angle of elevation.
06:07We will calculate speed from here.
06:12If distance is 87.17 and time is 120 seconds,
06:22then speed will be 0.73 m per second.
06:28This is the answer.