Question

a skydiver is dropped out of an airplane at an altitude of 10000 feet. she reaches a terminal velocity 60 seconds later. consider four positions during her fall. a: initial state (t = 0 seconds) b: 15 seconds after drop c: 45 seconds after drop d: 60 seconds after drop toggle through the set of vector diagrams at the right to identify the relative magnitude of the net force vector for each of these four positions. (consider vertical motion only.)

Explanation:

Step1: Analyze Initial State (A: t=0)

At \( t = 0 \), the skydiver is just dropped, so the only vertical force is gravity (\( F_g \)) downward, and air resistance (\( F_{air} \)) is 0 (since velocity is 0 initially). Net force \( F_{net}=F_g - F_{air}=F_g \) (downward), so the net force vector has magnitude equal to \( F_g \).

Step2: Analyze 15 Seconds (B: t=15)

After 15 seconds, the skydiver is accelerating downward, so velocity is increasing. Air resistance \( F_{air} \) is proportional to velocity (or velocity squared, depending on model), so \( F_{air}F_{air} \)).

Step3: Analyze 45 Seconds (C: t=45)

As time approaches 60 seconds (terminal velocity), velocity is closer to terminal velocity, so \( F_{air} \) is closer to \( F_g \). Net force \( F_{net}=F_g - F_{air} \) is smaller than at t=15 (since \( F_{air} \) is larger now).

Step4: Analyze 60 Seconds (D: t=60)

At terminal velocity, the skydiver's velocity is constant, so acceleration is 0. By Newton's second law, \( F_{net}=ma = 0 \). So net force magnitude is 0 (since \( F_g = F_{air} \), they cancel).

Answer:

• A (t=0): Net force magnitude = \( F_g \) (only gravity, no air resistance yet).
• B (t=15): Net force magnitude \( < F_g \) (gravity > air resistance, still accelerating down).
• C (t=45): Net force magnitude \( < \) magnitude at B (air resistance closer to gravity, less net force).
• D (t=60): Net force magnitude = 0 (terminal velocity, forces balance).

(To match with vector diagrams, identify: A has net force equal to gravity, B has smaller net force than A, C has smaller than B, D has net force 0.)