20070914, 15:13  #1 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
Projected Pictures.
When a screen is placed 10 feet from a projector, the picture occupies 10 sq.ft. How large will the picture be when the projector is 15 feet from the screen? Mally 
20070914, 15:32  #2 
Jun 2003
The Texas Hill Country
1089_{10} Posts 
How about
"10 sq ft" because that is the size of the screen. or There will be no picture at all because the power cord isn't long enough to reach the mains. 
20070914, 15:45  #3 
Oct 2005
Fribourg, Switzerlan
2^{2}·3^{2}·7 Posts 
15ft :)

20070914, 17:16  #4 
Jun 2003
7·167 Posts 
22.5 sq. feet.

20070914, 23:12  #5 
Cranksta Rap Ayatollah
Jul 2003
641 Posts 

20070915, 04:09  #6 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·3·1,013 Posts 
2.0903184 m^2

20070915, 07:22  #7 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Tricky solutions.
Well Victor, the others were right including Wacky with his lateral thinking. Retina gave a tricky conversion from sq. ft to sq. metres. Mr. P1 and OT were on the dot too. To be honest I was bowled over too ! You see, you cannot compare linear feet with square feet. One has to square the linear feet into square feet. Thus 10^2 = 100 sq.ft. 15^2 =225 sq.ft. Then set up the proportion 10 : 100 = x : 225 Thus x = 22.5 sq.ft. Hence the picture will have an area of 22.5 sq.ft. when the projector is 15 ft from the screen. Mally 
20070915, 07:57  #8  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×3×1,013 Posts 
Quote:


20070915, 08:18  #9 
"Lucan"
Dec 2006
England
194A_{16} Posts 
Note that "10 sq.ft." <> "10 ft square"

20070915, 08:33  #10 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
Optics
Treat the projector as a simple convex lens,
and take the distance of the screen to be measured from the optical centre of this lens. If we assume the images are accurately focussed, then we find that the object slide/film is closer to the lens for an image distance of 15 feet. So the angle subtended is larger in the second case giving a larger image than you have all been assuming. David Last fiddled with by davieddy on 20070915 at 08:38 
20070915, 10:40  #11 
Oct 2005
Fribourg, Switzerlan
2^{2}×3^{2}×7 Posts 

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