a skydiver is dropped out of an airplane at an altitude of 10000 feet. she reaches a terminal velocity 60…

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.)

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.)

Answer

Explanation:

Step1: Analyze Initial State (A)

At ( t = 0 ) seconds, the skydiver is just dropped, so initial velocity ( v_A = 0 ) (since she starts from rest).

Step2: Analyze 15 Seconds (B)

During free - fall (before terminal velocity), the skydiver is accelerating due to gravity. So ( v_B ) is positive (downward) and increasing, but ( v_B<v_D ) (since terminal velocity is reached at 60s) and ( v_B < v_C) (as time increases towards 60s, velocity increases towards terminal velocity). Also, ( v_B>v_A = 0 ).

Step3: Analyze 45 Seconds (C)

At 45 seconds, the skydiver is still accelerating towards terminal velocity (since terminal velocity is at 60s). So ( v_C) is greater than ( v_B ) (because more time has passed for acceleration) and less than ( v_D ) (since terminal velocity is the maximum velocity reached at 60s).

Step4: Analyze 60 Seconds (D)

At 60 seconds, the skydiver reaches terminal velocity. Terminal velocity is the constant velocity when the force of air resistance equals the force of gravity. So ( v_D ) is the maximum velocity among the four states, and ( v_D>v_C>v_B>v_A = 0 ).

Answer:

The relative magnitudes of the velocity vectors are ( v_A = 0), ( v_B<v_C<v_D ), with ( v_D ) being the largest (terminal velocity), ( v_C ) larger than ( v_B ), and ( v_A ) (initial) being zero. If we were to order the velocity magnitudes from least to greatest: ( A < B < C < D ).