Question

you have been asked to design the first ascent and drop for a new roller coaster. you decide to make the slope of the ascent 0.7 and the slop of the drop -1.8 and you decide to connect these two straight streches L1(x) and L2(x) with part of a parabola y=f(x), where f(x)=ax^2+bx+c where x and f(x) are measured in feet. for the track to be smooth there can't be any abrubt changes in direction, so you want the linear segments L1 and L2 to be tangent to the parabola at the transition points( call them p and q) assume p is at the origin and q is 100 feet away horizontally from p. find a,b,c

Answer 1

you have been asked to design the first ascent and drop for a new roller coaster. you decide to make the slope of the ascent 0.7 and the slop of the drop -1.8 and you decide to connect these two straight streches L1(x) and L2(x) with part of a parabola y=f(x), where f(x)=ax^2+bx+c where x and f(x) are measured in feet. for the track to be smooth there can't be any abrubt changes in direction, so you want the linear segments L1 and L2 to be tangent to the parabola at the transition points( call them p and q) assume p is at the origin and q is 100 feet away horizontally from p. find a,b,c