A parachutists fall from aeroplane after 5 seconds parachute opens and then retards find acceleration-time graph

To analyze the motion of a parachutist who falls from an airplane, we need to consider two distinct phases: the free fall before the parachute opens and the descent with the parachute deployed. Let's break this down step by step to create an acceleration-time graph for the entire scenario.

Phase 1: Free Fall

Initially, when the parachutist jumps from the airplane, they experience free fall due to gravity. The acceleration during this phase is constant and equal to the acceleration due to gravity, which is approximately 9.81 m/s² downward. This means that for the first 5 seconds, the acceleration-time graph will show a constant value.

Graph Representation

• From time 0 to 5 seconds, the acceleration is -9.81 m/s² (the negative sign indicates the downward direction).

Phase 2: Parachute Deployment

At the 5-second mark, the parachute opens. This drastically changes the dynamics of the fall. The parachute creates a significant amount of drag, which retards the downward motion of the parachutist. The acceleration during this phase will be negative but less than the acceleration due to gravity, as the parachutist is still descending but at a decreasing rate.

Acceleration After Parachute Opens

Once the parachute is deployed, the acceleration can vary depending on several factors, including the size of the parachute and the weight of the parachutist. However, for simplicity, let’s assume the parachute provides a constant deceleration of about 3 m/s² downward. Thus, the effective acceleration after the parachute opens can be calculated as follows:

• Effective acceleration = Acceleration due to gravity - Drag force from parachute
• Effective acceleration = -9.81 m/s² + 3 m/s² = -6.81 m/s²

Final Acceleration-Time Graph

Now, we can summarize the acceleration-time graph:

• From 0 to 5 seconds: Constant acceleration at -9.81 m/s².
• From 5 seconds onward: Constant acceleration at -6.81 m/s².

Visualizing the Graph

In a graphical representation, you would see a horizontal line at -9.81 m/s² from 0 to 5 seconds, and then a horizontal line at -6.81 m/s² starting from the 5-second mark onward. This change in the graph clearly indicates the moment the parachute opens and the reduction in acceleration due to the drag force acting against gravity.

Conclusion

Understanding the acceleration-time graph of a parachutist involves recognizing the two distinct phases of the fall: free fall under gravity and the subsequent descent with the parachute deployed. Each phase has its own characteristics, which are reflected in the graph. This analysis not only helps in visualizing the motion but also provides insights into the forces acting on the parachutist during the jump.