Question

a skydiver steps out of an airplane. the velocity-time graph shows how her velocity changes with time. (note: down is defined as the + direction of velocity.) at what points during the skydive does she experience the greatest, a zero, and the smallest (but non-zero) air resistance? tap on the fields below to toggle through the answer options. air resistance is greatest at -- air resistance is zero at -- air resistance is least (but not zero) at a

Explanation:

Step1: Recall air resistance and velocity

Air resistance \( F_{air} \) is proportional to velocity (for non - turbulent flow, \( F_{air}\propto v \), and for higher speeds, \( F_{air}\propto v^{2} \)). Also, from Newton's second law, the net force \( F_{net}=mg - F_{air}=ma \), where \( m \) is mass, \( g \) is acceleration due to gravity, and \( a \) is acceleration. The slope of the velocity - time graph gives acceleration (\( a=\frac{\Delta v}{\Delta t} \)).

Step2: Analyze point A

At point A, the skydiver just steps out of the plane. The velocity \( v = 0 \). So, \( F_{air}=0 \) (since \( F_{air}\) depends on velocity). So air resistance is zero at A.

Step3: Analyze point D

At point D, the velocity - time graph has a slope of zero (constant velocity, terminal velocity). So acceleration \( a = 0 \). From \( F_{net}=mg - F_{air}=ma = 0 \), we get \( F_{air}=mg \). Also, the velocity at D is the maximum (since the graph levels off here). Since \( F_{air}\) is related to velocity, at D, the velocity is maximum, so air resistance is maximum.

Step4: Analyze point B

We know that air resistance is non - zero (so not at A) and we need the least non - zero. The velocity at B is less than at C and D. Since \( F_{air}\) is related to velocity, a smaller velocity means a smaller air resistance (but non - zero, since velocity is non - zero at B). Wait, but let's re - check. Wait, the least non - zero: at B, the velocity is more than at A (where it's zero) and less than at C and D. So air resistance at B is more than at A (but A is zero) and less than at C and D. Wait, no, the third part was given as A is wrong. Wait, let's correct.

Wait, the key is:

• Air resistance is zero when velocity is zero (point A), because \( F_{air}\propto v \) (or \( v^{2} \)), so \( v = 0\Rightarrow F_{air}=0 \).

• Air resistance is greatest when velocity is maximum (terminal velocity, point D), because \( F_{air}\) increases with velocity (and at terminal velocity, \( F_{air}=mg \), which is the maximum it can be during the skydive as velocity stops increasing).

• Air resistance is least (but non - zero) when velocity is the smallest non - zero value. Looking at the graph, point B has a smaller velocity than C and D, and non - zero (since A is zero). Wait, but the original third box had A, which is wrong because at A, air resistance is zero. So the least non - zero is at B? Wait, no, let's re - do:

1. Air resistance is zero at A (velocity = 0, so \( F_{air}=0 \)).

1. Air resistance is greatest at D (terminal velocity, maximum velocity, so maximum \( F_{air}\) as \( F_{air}\) depends on velocity).

1. Air resistance is least (but non - zero) at B (velocity at B is less than at C and D, so \( F_{air}\) is less than at C and D, and non - zero since velocity is non - zero at B).

Answer:

• Air resistance is greatest at D.
• Air resistance is zero at A.
• Air resistance is least (but not zero) at B.