Final answer:
True, knowledge of initial positions and directions of motion for the elevator and miners is required to determine relative positioning and is essential for solving mechanics problems in physics.
Step-by-step explanation:
To calculate the position of the elevator relative to the surface, it is indeed true that we need to know the initial positions and the directions of motion of both the elevator and the miners. Understanding the initial conditions, such as position and velocity, allows us to predict the subsequent motion of the objects in question, according to the laws of physics. In the context of the elevator and miners, whether the elevator is accelerating upwards or downwards, or moving with a constant velocity, can critically affect calculations of work done by workers and the overall motion and displacement of the objects involved.
Furthermore, particulars such as the height of the second floor and the amount of work necessary to move a crate given the coefficients of kinetic friction on different floors are key to solving problems in mechanics. These examples illustrate how critical an understanding of initial conditions and the direction of motion are for accurately determining the motion of objects in physics problems.