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# Geometry Question

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An oil tanker is entering the Bay of Niteall near the seaside towns of Lazyville and Sleepyton. The oil tanker is due north of Sleepyton and due east of Lazyville. In order to determine the distance to shore, the communications officer, Elmer Mudd, sends out a blast on the fog horn. The horn automatically signals a light to flash back to the ship from the light towers in each town as soon as the sound strikes the sound sensors in the towers. It took 6 sec for the sound to reach Lazyville and 8 sec to reach Sleepyton. Elmer was able to calculate not only the distance from the ship to each town

Guest Feb 4, 2015

#3
+93691
+10

This was a really good question to make a person sort out the relevant info from the irrelevant info.

I liked it.

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You need the speed of sound to work out how long it took for the lighthouse to hear the horn

the speed of sound is 340.29m/sec

You need the speed of light to work our how long it takes for the return the flash of light.

Speed of light is 299797458m/s        This is so fast that I am going to ignore it and say that it is instantaneous.

in 8 sconds  the sound will travel    8*340.29 metres          $${\mathtt{340.29}}{\mathtt{\,\times\,}}{\mathtt{8}} = {\mathtt{2\,722.32}}$$

so the boat is 2.722 km from Sleepyton.

in 6 seconds it will travel              6*340.29 metres          $${\mathtt{340.29}}{\mathtt{\,\times\,}}{\mathtt{6}} = {\mathtt{2\,041.74}}$$

so the boat is 2.041 km from Lazyville.

Melody  Feb 4, 2015
#1
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sorry I don't know the answer!

Guest Feb 4, 2015
#2
+93691
0

Well then do not bother answering!

Melody  Feb 4, 2015
#3
+93691
+10

This was a really good question to make a person sort out the relevant info from the irrelevant info.

I liked it.

----------------------------------------------------------------

You need the speed of sound to work out how long it took for the lighthouse to hear the horn

the speed of sound is 340.29m/sec

You need the speed of light to work our how long it takes for the return the flash of light.

Speed of light is 299797458m/s        This is so fast that I am going to ignore it and say that it is instantaneous.

in 8 sconds  the sound will travel    8*340.29 metres          $${\mathtt{340.29}}{\mathtt{\,\times\,}}{\mathtt{8}} = {\mathtt{2\,722.32}}$$

so the boat is 2.722 km from Sleepyton.

in 6 seconds it will travel              6*340.29 metres          $${\mathtt{340.29}}{\mathtt{\,\times\,}}{\mathtt{6}} = {\mathtt{2\,041.74}}$$

so the boat is 2.041 km from Lazyville.

Melody  Feb 4, 2015