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Math Question - Answer Seems Unreal !!
13 Answers
A perfectly horizontal metal handrail constructed across the USA between Baltimore, Maryland and San Francisco in California measures 2,580 miles long. The chief engineer on the project informs you that in the summer the handrail will expand by just 1 inch (1") and will buckle upwards. Find how far a pedestrian has to reach up to stay in contact with the handrail at the half way point. Important Note: Ignore the curvature of the earth.
Answers
753.3923264 feet approx If I made a mistake, I'm not doing it again!
11:38 Mon 05th Jun 2023
When it buckles an isosceles triangle is formed. You need the height at the midpoint.
The distance between Baltimore and the midpoint = 1290 miles
The hypotenuse of the triangle Baltimore, Midpoint, Height = 1290 miles andhalf an inch
Half an inch = 1/12672 miles
Square the hypotenuse and subtract the square of the base
Square root the remainder
and that = my answer!
The distance between Baltimore and the midpoint = 1290 miles
The hypotenuse of the triangle Baltimore, Midpoint, Height = 1290 miles andhalf an inch
Half an inch = 1/12672 miles
Square the hypotenuse and subtract the square of the base
Square root the remainder
and that = my answer!
//// 753.3923264 feet approx
If I made a mistake, I'm not doing it again! ////
I didn't believe it, so I worked it out myself and got the same answer:
Same as JJ109 but I converted to inches.
1 mile = 63 360 inches.
Halfway point = 1290 x 63 360 = 81 734 400"
Triangle formed with hypotenuse = 81 734 400.5"
and base = 81 734 400"
Height of hypotenuse triangle = H
H = Sq Root ((81 734 400.5)^2 - (81 734 400)^2)
H = Sq Root (81 700 000)
H = 9038.88"
H = 753.23 feet
Wowzer !!!!
If I made a mistake, I'm not doing it again! ////
I didn't believe it, so I worked it out myself and got the same answer:
Same as JJ109 but I converted to inches.
1 mile = 63 360 inches.
Halfway point = 1290 x 63 360 = 81 734 400"
Triangle formed with hypotenuse = 81 734 400.5"
and base = 81 734 400"
Height of hypotenuse triangle = H
H = Sq Root ((81 734 400.5)^2 - (81 734 400)^2)
H = Sq Root (81 700 000)
H = 9038.88"
H = 753.23 feet
Wowzer !!!!
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