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 velocity vector for each of these four positions. (consider vertical motion only.)

Explanation:

Step1: Understand Terminal Velocity

Terminal velocity is the constant velocity reached when the drag force equals the gravitational force. Before reaching terminal velocity (at \( t = 60 \) s), the skydiver is accelerating downward, so velocity magnitude increases with time until \( t = 60 \) s (terminal velocity, constant magnitude).

Step2: Analyze Each Position

• Position A (\( t = 0 \) s): Initial velocity is \( 0 \) (dropped, not thrown), so velocity magnitude \( v_A = 0 \).
• Position B (\( t = 15 \) s): Still accelerating (before terminal velocity), velocity magnitude \( v_B \) is greater than \( 0 \) but less than at \( t = 45 \) s and \( t = 60 \) s.
• Position C (\( t = 45 \) s): Still accelerating (before \( t = 60 \) s), velocity magnitude \( v_C \) is greater than \( v_B \) but less than \( v_D \) (since terminal velocity is reached at \( t = 60 \) s, \( v_D \) is constant and maximum for \( t \geq 60 \) s).
• Position D (\( t = 60 \) s): Terminal velocity reached, so velocity magnitude \( v_D \) is constant (and greater than \( v_B, v_C \) since it's the maximum steady velocity).

Step3: Rank Velocity Magnitudes

From least to greatest: \( v_A (0) < v_B < v_C < v_D \) (since acceleration is downward until terminal velocity, velocity increases with time until \( t = 60 \) s, then stays constant). So the velocity vector magnitudes follow \( |\vec{v}_A| < |\vec{v}_B| < |\vec{v}_C| < |\vec{v}_D| \).

Answer:

The relative magnitude of the velocity vectors (vertical motion) is \( |\vec{v}_A| < |\vec{v}_B| < |\vec{v}_C| < |\vec{v}_D| \), meaning at \( t = 0 \) (A) velocity is 0, then increases at 15s (B), 45s (C), and is constant (terminal) at 60s (D).