Question

a skydiver steps out of an airplane. the velocity - time graph shows how his velocity changes with time. (note: down is defined as the + direction of velocity.) match each of the free - body diagrams to one of the points on the graph.

Explanation:

Step1: Analyze Point A

At point A (time = 0, just stepping out), air resistance \( F_{air} \) is 0 (since velocity is 0, no air resistance yet). So \( F_{grav} > F_{air} \) (here \( F_{air} = 0 \)). The second free - body diagram (from left) has \( F_{air} \) much smaller than \( F_{grav} \), so it matches A.

Step2: Analyze Point B

At point B, the skydiver is accelerating, so net force is downward (\( F_{grav}>F_{air} \)). The first free - body diagram (from left) has \( F_{grav} > F_{air} \) (but \( F_{air} \) is non - zero now), so it matches B.

Step3: Analyze Point C

At point C, the skydiver is still accelerating but the acceleration is decreasing (slope of v - t graph is decreasing). So \( F_{grav}>F_{air} \), but \( F_{air} \) is closer to \( F_{grav} \) than at B. The third free - body diagram (from left) has \( F_{air} \) closer to \( F_{grav} \) than the first, so it matches C.

Step4: Analyze Point D

At point D, the skydiver has reached terminal velocity, so net force is zero (\( F_{grav}=F_{air} \)). The fourth free - body diagram (from left) has \( F_{air} = F_{grav} \), so it matches D.

Answer:

• Point A: Second free - body diagram (from left)
• Point B: First free - body diagram (from left)
• Point C: Third free - body diagram (from left)
• Point D: Fourth free - body diagram (from left)