Posted on 2003-03-22
A doorway is to be parabolic in shape and 2 metres high. At the height of 1 metre above ground level the width of the opening is 1.6 metres. How wide is the door at floor level.
I worked this out to be (8 * Sqrt(2)) / 5 or 2.2627 metres, but I don't think I did it the most effecient way.
You see, At Y = 1 we are told that there difference between the two x intcpts is 1.6metres and at y =2 the distance between them is 0 (because it is a turning point)
So I made up the equation Y = ax(x-b) and substitued Y = 1. Factorised it and once I got to the factorisation and I worked out the distance between the two x intctps was equal to 1.6.. THen I solved this for A and still had a B in the equation, so I did the same for Y=2. Then Once I had to equations in A=.... equations in terms of B I solved them simulataneously to find B, put B back into an equation to find A and found the equation to beY = 25/16x(X-(8*Sqr(2))/5))
Anyway, the x int was easy from there.
I think there must be an easier way.
I also realise that the parabola was supposed to be negative, for some reason A turned out to be 25/16 instead of -(25/16)
I am not sure why this is.
Could someone please tell me the proper way to do this problem because I think there has to be an easier way.