Final answer:
The student's homework question pertains to the physics of a bow and arrow, specifically calculating the arrow's speed using Hooke's Law and energy conservation. Given the force and displacement, one can find the spring constant and then use it to determine the arrow's kinetic energy and ultimately its launch speed.
Step-by-step explanation:
The question relates to the minimum allowable draw weight for a bow used to hunt big game animals. However, the provided information is for a physics problem about calculating the speed of an arrow shot from a bow, which can be solved using Hooke's Law for springs and the conservation of energy.
We're given that an archer pulls back the bow 50 cm (0.50 meters) with a force of 150 N. If we assume Hooke's Law applies, the spring constant k can be found using the formula F = kx where F is the force applied, k is the spring constant, and x is the displacement from the equilibrium position. Once k is found, the potential energy (PE) stored in the 'spring' can be calculated using PE = (1/2)kx^2.
This energy is then converted to kinetic energy (KE) of the arrow when it is released. Assuming no other forces act on the system (like friction and air resistance), the full amount of potential energy converts to kinetic energy. The formula for KE is KE = (1/2)mv^2 where m is the mass of the arrow and v is its velocity. By equating PE to KE, we can solve for the speed of the arrow, v.