Final answer:
Skydivers initially experience an acceleration of 9.81 m/s² due to gravity. As they fall, air resistance increases, causing a decrease in acceleration until they reach terminal velocity, where it approaches zero. Terminal velocity varies with body position and drag, and can be calculated using assumptions on frontal areas.
Step-by-step explanation:
The acceleration of two falling skydivers is greatly influenced by both gravity and air resistance. At the start of their fall, the skydivers experience acceleration due to gravity, which is approximately 9.81 m/s². However, as they fall faster, they encounter air resistance, which grows with the square of their velocity, leading to a decrease in acceleration.
As the skydivers continue to fall, they approach their terminal velocities, the point where the force due to air resistance equals the force of gravity, and their acceleration towards Earth reduces to essentially zero. The shape of the graph depicting the magnitude of acceleration versus time starts with a constant value (9.81 m/s²), then decreases as the skydivers pick up speed until it flattens out upon reaching terminal velocity.
For a skydiver with a mass of 75 kg, the terminal velocity can be about 350 km/h in a headfirst position. However, this speed can be reduced to approximately 200 km/h in a spread-eagle position due to an increase in the frontal area and, subsequently, drag. If the skydiver opens a parachute, the terminal velocity decreases further because of the additional drag.
Given the relevant physics principles, it is possible to calculate their terminal velocities by making assumptions about their frontal areas and using the drag equation. The time it takes for each skydiver to reach the ground assuming a small time to reach terminal velocity can be estimated using kinematic equations, factoring in the initial altitude and the constant acceleration of gravity prior to reaching terminal velocity.