Final answer:
The force a 50.0-kg woman must exert on the floor with each hand during a push-up at constant speed is approximately 245 N, which is half of her total weight force, assuming equal weight distribution.
Step-by-step explanation:
To determine the force a 50.0-kg woman must exert on the floor with each hand during a push-up, we must consider her weight and how that weight is distributed while she performs a push-up. Since the woman moves at a constant speed, there is no acceleration and the forces are in equilibrium. The woman's weight, which is the force due to gravity, is equal to her mass multiplied by the acceleration due to gravity (9.8 m/s2). This gives a total weight force (Fw) of 50.0 kg * 9.8 m/s2, which equals 490 N.
Assuming her body is evenly distributed, and ignoring additional factors such as arm position for simplicity, the force that must be exerted on the floor by each hand would be half of her weight force. Thus, the force per hand is 490 N / 2 which equals 245 N.
It is important to note that this is a simplification and actual values may vary based on the distribution of weight in her body and the position of her arms and feet during the push-up.