Let and be two parabolas with the same coefficient for the term. The y-intercepts of the two parabolas are and respectively. Let the two parabolas intersect at and let the tangent to the two parabolas drawn at and intersect at . Show using physics that .
Hint: Assume x is time and y is space, and there is acceleration due to gravity of a/2 in this 1-d space. View objects first in an inertial frame, and then in an accelerated frame of reference accelerating forward at a/2.