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

Answer

Explanation:

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

At ( t = 0 ), the skydiver has just been dropped. The only vertical force is gravity (( F_g )) downward, and air resistance (( F_{air} )) is 0 (since velocity is 0 initially). So net force ( F_{net}=F_g - F_{air}=F_g ) (downward), 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 is proportional to velocity (or velocity squared, but for relative magnitude, we know ( F_{air}<F_g )) because net force is still downward (( F_{net}=F_g - F_{air}>0 )). So ( F_{net} ) magnitude is less than at ( t = 0 ), but still positive (downward).

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

As time approaches 60 seconds (terminal velocity), velocity is closer to terminal velocity, so air resistance is closer to ( F_g ). But since terminal velocity is reached at ( t = 60 ), at ( t = 45 ), ( F_{air}<F_g ) (because still accelerating, though acceleration is decreasing). So ( F_{net}=F_g - F_{air} ), magnitude is smaller than at ( t = 15 ) (since ( F_{air} ) is larger at ( t = 45 ) than at ( t = 15 )).

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

At terminal velocity, the skydiver is moving at constant velocity, so net force is 0 (( F_{net}=F_g - F_{air}=0 )), meaning ( F_{air}=F_g ) in magnitude (opposite direction). So net force magnitude is 0.

Relative Magnitudes:

  • A: ( F_{net}=F_g ) (largest)
  • B: ( F_{net}=F_g - F_{air1} ) ( ( F_{air1}<F_{air2}<F_g ) where ( F_{air2} ) is at ( t = 45 ))
  • C: ( F_{net}=F_g - F_{air2} ) (smaller than B, since ( F_{air2}>F_{air1} ))
  • D: ( F_{net}=0 ) (smallest)

So the order of net force magnitude (from largest to smallest) is ( A > B > C > D ), and at D, net force is 0.

Answer:

  • A: Net force magnitude = ( F_g ) (downward)
  • B: Net force magnitude ( < F_g ), downward
  • C: Net force magnitude ( < B ), downward
  • D: Net force magnitude = 0