Final answer:
An archer's arrow's range is determined by the initial kinetic energy transferred from the applied force and the draw distance, combined with the projectile motion. However, with the provided data, a complete solution cannot be given without the arrow's initial velocity or considering air resistance.
Step-by-step explanation:
The problem in question involves finding out how far an arrow will land from the archer when shot horizontally from a certain height. To solve this problem, we need to consider two main aspects: the work done on the arrow by the archer and the projectile motion of the arrow. The work done is essentially the energy transferred to the arrow, given by the product of the force exerted and the distance over which it is applied (Work = Force x Distance). This energy then becomes the kinetic energy of the arrow. The horizontal distance covered by the arrow (range) will depend on its initial horizontal velocity and the time it takes to fall to the ground due to gravity.
Using the given force of 390 N and the draw distance of 0.75 m, we can calculate the initial kinetic energy of the arrow. However, without the initial velocity or further details on the drag or air resistance, we cannot accurately calculate the distance. Typically, this would also require the use of the equation of motion for projectile motion. But since this isn't a complete set of data, we would need more information to provide an answer.