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# How to setup Related Rates problem?

Posted on 2014-10-19
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A flood light is on the ground 45 meters from a building.  A thief 2 meters tall runs from the floodlight directly towards the building at 6 m/sec.  How rapidly is the length of this shadow on the building changing when he is 15 meters from the building ?

This is problem from first calculus course taught in a University.  This is a related rates problem.

Please help setup this problem.  Is this going to be a triangle?  15 meters from building might be one side of the triangle.  Change of length of shadow on building might be another side of triangle.  What would be the hypotenuse?

Is flood light projected at an angle on the bulding?
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Question by:naseeam
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2nd earned 500 total points
ID: 40390932
It says the floodlight is on the ground, so I would have the feet of the thief and the base of the wall also on the ground. Project from the lamp through the 2m height to the wall and calculate the height of the shadow. This is based on the changing distance of the 2m height from the lamp.  He runs at a constant speed so you need to find the change in height of the shadow at the 15m point. The shadow is getting shorter.
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Expert Comment

ID: 40390936
Hypotenuse is the projected line from the lamp through his head up to the wall. The 2m height and the wall are two verticals at 90° to the ground.
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Expert Comment

ID: 40390940
Just remembered another key word. There are two similar triangles. One 2 metres high and the base increasing at 6m/s. The other with a fixed base of 45m and a varying height.
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Author Comment

ID: 40391177
All of this information should help us solve the problem.  We'll solve it tomorrow evening.
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