Final answer:
The skydiver was in free fall for approximately 9 seconds before reaching an instantaneous velocity of 88.2 meters per second, calculated using the formula t = (V - V0)/a with the acceleration due to gravity.
Step-by-step explanation:
To determine how long the skydiver was in free fall before reaching an instantaneous velocity of 88.2 meters per second, we must consider the acceleration due to gravity and the forces involved. During the first 2 seconds, the skydiver accelerates at 9.8 m/s², which gives a speed of 19.6 m/s after 2 seconds. Assuming that for the remainder of the time until the parachute is deployed, the skydiver is falling with a constant acceleration of 9.8 m/s², we can use the kinematic equation:
V = V0 + at
Where V is the final velocity (88.2 m/s), V0 is the initial velocity (0 m/s, as the skydiver starts from rest), a is the acceleration (9.8 m/s²), and t is the time in seconds. Rearranging the equation to solve for t gives:
t = (V - V0)/a
t = (88.2 m/s) / (9.8 m/s²)
t ≈ 9 seconds
Therefore, the skydiver was in free fall for approximately 9 seconds before reaching the velocity of 88.2 m/s.