Final answer:
The time and position of the intersection of the rocket and flare paths can be found by solving a system of equations representing their respective paths.
Step-by-step explanation:
To determine the time and position at which the rocket and flare paths intersect, you would use solving a system of equations. Both paths can be represented by equations in terms of position and time. By setting these equations equal to each other, you can solve for the point of intersection, which gives you the time at which they intersect as well as their position at that time.
Although measuring time, observing heights, and analyzing areas under velocity-time graphs do provide information about the motions involved, these methods do not directly provide an intersection point of two different paths. The appropriate method is to apply the kinematic equations that relate time, velocity, and position, recombine the horizontal and vertical components of motion, and solve the corresponding system of equations to find the intersection point.