Final answer:
In Physics, Projectile Motion is analyzed to determine the distance traveled by a projectile. The total distance is the sum of vertical and horizontal components, and for motion straight up, it is twice the ascent distance if the projectile returns to the launch height within the time interval.
Step-by-step explanation:
The subject of the question pertains to Projectile Motion, which is a concept in Physics where an object is thrown near the Earth's surface, and it moves along a curved path under the action of gravity only. To determine the total distance traveled by a projectile during a time interval, one needs to consider both the vertical and horizontal components of the projectile's motion. If a projectile is launched straight up with an initial velocity and does not land within a certain time interval, its total distance traveled will simply be twice the distance it rises until it stops momentarily at its peak (if we are considering that the time interval includes the ascent and descent).
As the projectile ascends, it decelerates due to gravity, until its vertical velocity becomes zero at its peak. The distance it covers during the ascent can be found using the kinematic equation for uniformly accelerated motion. Once the projectile starts its descent, it will cover the same vertical distance as it ascends if it returns to the same initial height from which it was launched. Therefore, the total vertical distance traveled by the projectile during the entire ascent and descent will be twice the ascent distance. The horizontal distance can be calculated separately using the constant horizontal velocity provided the projectile has an initial horizontal component.