Kaiser Imperial
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Kaiser Imperial
In world war 1 the imperial german army developed a piece of artillery called Big Bertha.?
When the barrel was elevated to an angle of 45 degrees, a shell fired from this monstrosity would supposedly travel 72 miles. Assuming a parabolic trajectory, and neglecting air resistance, curvature of earth, the curvature of Kaiser's moustache, etc. , how maximally far above the earth's surface did the shell get???
y=a*x^2+bx+c
dy/dx=2ax+b
want dy/dx at x=0 to be 1... this will give the 45 degree elevation:
b=1
want dy/dx at x=72 to be -1... symmetry
2a*72+1=-1
a=-1/72
Our parabola is
y=-1/72*x^2 + x +c
max height is when dy/dx is zero:
-2/72*x+1=0
x=1*72/2=36 (could have gotten this by symmetry also, reaches peak
at half way mark)
plug in 36 to parabola , y=18 miles
What happened to c?... well it shouldn't have been there in the first place, because
it would have meant that we launched at c miles above the ground; so
of course, the shell would have reached its peak 18+c miles above the ground.
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