To calculate the volume of the athlete, divide the athlete's weight by the density of water. The buoyant force exerted by air can be found by multiplying the density of air by the volume of the athlete. The ratio of the buoyant force to the weight of the athlete is 0.0012.
Step-by-step explanation:
To calculate the volume of the athlete, we first need to determine the density of the athlete. Density is mass divided by volume. Given that the athlete's weight is 905 N and the upward force required to keep him from sinking is 20 N, the buoyant force is equal to the weight of the water displaced by the athlete. Using the equation for buoyant force, we can find the volume of the athlete. Since the athlete does not float, the buoyant force must be equal to the weight of the athlete. Therefore, the volume of the athlete is 905 N divided by the density of water, which is 1000 kg/m³. This gives a volume of 0.905 m³.
To find the buoyant force exerted by air on the athlete, we need to multiply the density of air by the volume of the athlete. The density of air is approximately 1.2 kg/m³. Multiplying this by the volume of the athlete, 0.905 m³, gives a buoyant force of 1.086 N.
The ratio of the buoyant force to the weight of the athlete can be calculated by dividing the buoyant force by the weight of the athlete. The buoyant force is 1.086 N and the weight of the athlete is 905 N, so the ratio is 1.086/905 = 0.0012.