A parachutist 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 understand how to construct the acceleration-time graph for this scenario.

Phase 1: Free Fall

Initially, when the parachutist jumps from the airplane, they experience free fall due to gravity. During this phase, the only force acting on them is gravity, which causes a constant acceleration downwards. This acceleration is approximately 9.81 m/s², directed towards the Earth.

Acceleration During Free Fall

• Time: 0 to 5 seconds
• Acceleration: 9.81 m/s²

On the acceleration-time graph, this phase will be represented as a horizontal line at the value of 9.81 m/s² from 0 to 5 seconds.

Phase 2: Parachute Deployment

After 5 seconds, the parachute opens. This event drastically changes the dynamics of the fall. The parachute creates a significant amount of drag, which opposes the force of gravity. As a result, the parachutist experiences a rapid decrease in acceleration.

Acceleration After Parachute Opens

• Time: 5 seconds onwards
• Acceleration: Negative (retardation)

When the parachute opens, the acceleration will drop sharply to a negative value, indicating deceleration. The exact value of this negative acceleration depends on factors such as the size of the parachute and the weight of the parachutist, but it can be approximated to around -5 m/s² for a typical parachute. This value means that the parachutist is slowing down as they descend.

Graph Representation

Now, let’s visualize the acceleration-time graph:

• From 0 to 5 seconds: A horizontal line at 9.81 m/s².
• At 5 seconds: A sharp drop to around -5 m/s².
• From 5 seconds onwards: A horizontal line at the negative acceleration value, indicating a constant rate of deceleration until the parachutist reaches terminal velocity.

Final Thoughts

In summary, the acceleration-time graph for the parachutist will show a constant positive acceleration during free fall, followed by a sudden drop to a negative acceleration when the parachute opens. This change reflects the transition from free fall to a slowed descent due to the parachute's drag force. Understanding these phases helps in visualizing how forces interact during a parachutist's fall.