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)

At \( t = 0 \) (initial state), the skydiver has just been dropped. The only force acting vertically is gravity (\( F_g \)) downward, and air resistance (\( F_{air} \)) is initially zero (since velocity is zero). So net force \( F_{net}=F_g - F_{air}=F_g \) (downward), magnitude equal to \( F_g \).

Step2: Analyze 15 Seconds (B)

After 15 seconds, the skydiver is accelerating downward, so velocity is increasing. Air resistance is proportional to velocity (or velocity squared, depending on model), so \( F_{air}>0 \) but less than \( F_g \). Thus, net force \( F_{net}=F_g - F_{air} \), magnitude is \( F_g - F_{air} \), which is less than \( F_g \) (from step 1) but greater than zero.

Step3: Analyze 45 Seconds (C)

As time approaches 60 seconds (terminal velocity), velocity is closer to terminal velocity, so \( F_{air} \) is closer to \( F_g \). At 45 seconds, \( F_{air} \) is larger than at 15 seconds, so \( F_{net}=F_g - F_{air} \) has a smaller magnitude than at 15 seconds (since \( F_{air} \) is closer to \( F_g \)).

Step4: Analyze 60 Seconds (D)

At 60 seconds, terminal velocity is reached. This means net force is zero (\( F_{net}=F_g - F_{air}=0 \)), so magnitude of net force is zero.

So the relative magnitudes of net force vectors (from largest to smallest) would be: \( A > B > C > D \) (since \( D \) has magnitude 0, \( C \) has smaller magnitude than \( B \), \( B \) smaller than \( A \)).

Answer:

The relative magnitude of net force vectors (from largest to smallest) is \( A > B > C > D \), with \( D \) having magnitude 0, \( C \) smaller than \( B \), \( B \) smaller than \( A \).