Question
a parabolic bridge over a road is 4 meter tall 4 meter wide and 5 meter long determain the maximum height of a 2 meter truck can drive under the bridge
Answers
Steve
I am assuming that your somewhat vague language means that the parabola can be described by
y = 4-ax^2
and that the parabola intersects the road below at x=2.5
So, y = 4-(16/25)x^2
Now, assuming you mean a truck which is 2m wide and is driving right down the center line, that means x=1, so
y(1) = 4 - 16/25 = 84/25 = 3.36m
If the truck is driving just to one side of the center line, that means x=2, and
y(2) = 4 - (16/25)(4) = 36/25 = 1.44m
I still can't factor in what "4m wide" means for the bridge. The width of the pavement? That makes no difference on level ground. The problem is very poorly worded.
y = 4-ax^2
and that the parabola intersects the road below at x=2.5
So, y = 4-(16/25)x^2
Now, assuming you mean a truck which is 2m wide and is driving right down the center line, that means x=1, so
y(1) = 4 - 16/25 = 84/25 = 3.36m
If the truck is driving just to one side of the center line, that means x=2, and
y(2) = 4 - (16/25)(4) = 36/25 = 1.44m
I still can't factor in what "4m wide" means for the bridge. The width of the pavement? That makes no difference on level ground. The problem is very poorly worded.