A parachutist jumps from a height of 5000 metres. The relationship between his falling speed ‘v’ and the distance fallen through ‘d’ is best represented as

The correct answer is Option 4 (Graph IV). This question tests the application of fluid dynamics and terminal velocity in a real-world scenario.

When a parachutist jumps, they are initially subject to the force of gravity, causing a rapid increase in velocity (v) as the distance (d) increases. However, as speed increases, air resistance (drag force) also increases. Eventually, the upward drag force equals the downward gravitational force. At this point, the net force becomes zero, and the parachutist reaches a constant speed known as terminal velocity.

• Initial Phase: The curve shows a sharp rise in velocity as the parachutist accelerates.
• Terminal Phase: The curve flattens out, becoming a horizontal line parallel to the distance axis, indicating that velocity remains constant regardless of further distance fallen.

Other options are incorrect because Graph I suggests constant acceleration, while Graphs II and III do not account for the stabilization of speed at terminal velocity, which is the defining characteristic of such a fall.