Final answer:
To solve the skydiver's fall, the speed when the parachute opens and the distance fallen can be obtained by analyzing the forces and integrating velocity over time. The terminal velocity is found when air resistance equals gravity, and the time in the air post-deployment is calculated using the remaining distance and terminal velocity.
Step-by-step explanation:
Calculations for a Skydiver's Fall
Let's address the student's questions one by one for a skydiver weighing 120 kg.
(a) Speed When the Parachute Opens
The skydiver accelerates due to gravity while the force of air resistance works against the fall. This can be described by the equation:
F = ma = mg - kv, where F is the net force, m is the mass (120 kg), g is the acceleration due to gravity (9.8 m/s2), k is the air resistance coefficient (-10 when the parachute is closed), and v is the velocity. The velocity at the moment the parachute opens can be found by solving the differential equation, which leads to an exponential model of velocity over time. We look for the velocity at 40 seconds.
(b) Distance Fallen Before the Parachute Opens
To find the distance fallen, integrate the velocity function from 0 to 40 seconds.
(c) Limiting or Terminal Velocity After Parachute Opens
The terminal velocity vL occurs when the force of air resistance equals the gravitational force, and acceleration ceases (ma = 0). With the parachute open, k = -120, so solving mg - kvL = 0 for vL will give the terminal velocity.
(d) Time in the Air After Parachute Opens
To find the time the skydiver is in the air after the parachute opens, calculate the remaining distance to fall after the chute has been deployed using the terminal velocity and the distance already fallen, then determine the time it would take to fall that remaining distance at terminal velocity.