22) An arch is in the shape of a parabola whose axis is vertically downwards and measures 80 mts across - Maths -

Question

22) An arch is in the shape of a parabola whose axis is
vertically downwards and measures 80 mts across its bottom on the
ground Its highest point is 24 mts The measure of the horizontal
beam across its cross section at a height of 18 mts is __
1) 50 2) 40 3) 45 4) 60​

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

Let axis of parabola be y-axisHence we havex2=-4ay-k negative sign because axis is vertically downwardsNow highest point is 24 mHence k=24⇒x2=-4ay-24Now parabola measures 80 mts across its bottom on the groun
Hence by symmetry 40,0 will lie on parabola⇒402=-4a0-24⇒4a=40×4024=160024=2003Hencex2=-2003y-24Now put y=18⇒x2=-200318-24⇒x2=-2003-6⇒x2=400⇒x=±20Hence length of horizontal beam=20+20=40 Answer

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22) An arch is in the shape of a parabola whose axis is vertically downwards and measures 80 mts across its bottom on the ground. Its highest point is 24 mts. The measure of the horizontal beam across its cross section at a height of 18 mts is __ 1) 50 2) 40 3) 45 4) 60​

22) An arch is in the shape of a parabola whose axis is vertically downwards and measures 80 mts across its bottom on the ground. Its highest point is 24 mts. The measure of the horizontal beam across its cross section at a height of 18 mts is __

1) 50 2) 40 3) 45 4) 60