A parachutist steps from an aircraft, falls freely for two second, and then opens his parachute. Which of the following acceleration time `(a - t)` graphs best represents his downward acceleration `a` during the first 5 second ?

Options

A.
B.
C.
D.

Explanation

To solve the problem of the parachutist's downward acceleration during the first 5 seconds, we need to analyze the motion in two distinct phases: the free fall before the parachute opens and the subsequent deceleration after the parachute opens.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- When the parachutist steps out of the aircraft, he is in free fall. This means he is only influenced by the force of gravity.
- The acceleration due to gravity (g) is approximately \(9.8 \, \text{m/s}^2\).

2. **Acceleration During Free Fall**:
- For the first 2 seconds, the parachutist falls freely. Therefore, his acceleration remains constant at \(9.8 \, \text{m/s}^2\).
- On a graph, this would be represented as a horizontal line at \(9.8 \, \text{m/s}^2\) from \(t = 0\) to \(t = 2\) seconds.

3. **Opening of the Parachute**:
- After 2 seconds, the parachutist opens his parachute. This action introduces an upward force (drag) that opposes the force of gravity.
- As a result, the net acceleration will decrease. The parachutist will experience a reduction in acceleration as the parachute opens and begins to slow him down.

4. **Acceleration After Opening the Parachute**:
- The acceleration will not immediately drop to zero but will gradually decrease from \(9.8 \, \text{m/s}^2\) to a lower value (which could be zero or a small positive value depending on the parachute's effectiveness).
- This decrease in acceleration will be represented on the graph as a downward slope starting from \(t = 2\) seconds and continuing until \(t = 5\) seconds.

5. **Final Representation on the Graph**:
- The graph will show:
- A constant acceleration of \(9.8 \, \text{m/s}^2\) for the first 2 seconds.
- A decreasing acceleration from \(9.8 \, \text{m/s}^2\) to a lower value (potentially approaching zero) from \(t = 2\) to \(t = 5\) seconds.

### Conclusion:
Based on the above analysis, the acceleration-time graph that best represents the downward acceleration of the parachutist during the first 5 seconds will show a constant value of \(9.8 \, \text{m/s}^2\) for the first 2 seconds, followed by a gradual decrease in acceleration until the 5-second mark.