Question

a skydiver is dropped out of an airplane at an altitude of 10000 feet. he reaches a terminal velocity 40 seconds later. consider four positions during his fall. a: initial state (t = 0 seconds) b: 10 seconds after drop c: 30 seconds after drop d: 40 seconds after drop toggle through the set of vector diagrams at the right to identify the relative magnitude of the acceleration vector for each of these four positions. (consider vertical motion only.)

Explanation:

Step1: Recall Terminal Velocity Concept

Terminal velocity is reached when the net force (and thus acceleration) becomes zero. At \( t = 0 \) (State A), the skydiver starts falling, so air resistance is minimal, and acceleration is close to \( g \) (acceleration due to gravity).

Step2: Analyze 10 Seconds (State B)

After 10 seconds, the skydiver is speeding up, but air resistance is less than weight. So net force (and acceleration) is still significant but less than at \( t = 0 \).

Step3: Analyze 30 Seconds (State C)

At 30 seconds, closer to terminal velocity (reached at 40s), air resistance is closer to weight. Net force (acceleration) is smaller than at 10s.

Step4: Analyze 40 Seconds (State D)

At terminal velocity (\( t = 40 \)s), net force is zero, so acceleration is zero.

So the order of acceleration magnitude (from largest to smallest) is: \( A > B > C > D \) (with \( D = 0 \)). To identify vector diagrams:

• For \( A \): Acceleration vector (downward) is large (since air resistance is negligible, net force = weight, \( a = g \)).
• For \( B \): Acceleration vector is smaller than \( A \) (air resistance opposes, net force = weight - air resistance, so \( a < g \)).
• For \( C \): Acceleration vector is smaller than \( B \) (closer to terminal velocity, air resistance closer to weight, net force smaller).
• For \( D \): Acceleration vector has magnitude 0 (no net force).

Answer:

The relative magnitude of acceleration vectors (from largest to smallest) is \( A > B > C > D \), with \( D \) having magnitude 0. When identifying vector diagrams:

• \( A \): Large downward acceleration vector.
• \( B \): Smaller downward acceleration vector than \( A \).
• \( C \): Smaller downward acceleration vector than \( B \).
• \( D \): Acceleration vector with magnitude 0 (no vector or zero-length vector).