







A railway bridge over a road is in the shape of a parabola 
20111123 

From Brennen: A railway bridge over a road is in the shape of a parabola,
and the bridge is 3 m high in the middle and 6 m wide at its base.
A truck that is 2m wide is approaching the bridge.
What is the maximum height that the truck can have and
still pass under the bridge? Explain.
Thank you!! Answered by Penny Nom. 





A tunnel from Toronto to Montreal 
20100125 

From Dave: I want to make a tunnel from Toronto to Montreal (for example)
Something like this
http://mathcentral.uregina.ca/QQ/database/QQ.09.09/h/grant1.html

My coordinates are 45.442455,73.861340 (Montreal) and 43.442455, 79.861340 (Toronto)
I need to know how to find arc distance, chord distance and radius
What websites can i find for this subject
Google has many but they are useless (blah blah) websites
LOL
Thanks Answered by Chris Fisher and Robert Dawson. 





How many feet tall is the tunnel 
20061014 

From Charles: A tunnel in the Smoky Mountains is semicircular. At a distance of 12 feet from the center of the tunnel, the tunnel has a height of 16 feet. How many feet tall is the tunnel at its center? Answered by Penny Nom. 





An elliptic tunnel 
20010324 

From Janna: A tunnel is built under a river for a road 12m wide with a 2m sidewalk on either side. The top of the tunnel is semielliptical. A local bylaw stipulates that there must be a clearance of at least 3.6m at all points on the road. If the smallest possible ellipse is used, find the clearance at the center of the road. Answered by Harley Weston. 





Running Through a Train Tunnel 
20000401 

From Eugene Chan: A man is running through a train tunnel. When he is 2/3 of the way through, he hears a train that is approaching the tunnel from behind him at a speed of 60 mph. Whether he runs ahead or back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in miles per hour, is he running? (Assume he runs at a constant rate.) I think the answer (12 mph) is wrong. Also, I believe it should read 1/3 of the way through, but don't know how to prove it. Could you come up with some way to prove it, please? I would really appreciate it. Answered by Penny Nom. 

