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Spec links: 4.5.1.3 Gravity (weight, W = mg) · 4.5.1.4 Resultant forces · 4.5.6.1.5 Acceleration and terminal velocity (velocity–time graphs for terminal velocity: Physics only) · 4.5.6.2.1 Newton’s First Law · 4.5.6.2.2 Newton’s Second Law · Reading time: about 4 minutes

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Stepping out of a plane

The door slides open. Wind roars past. Four kilometres below, the fields look like a patchwork quilt. Every weekend, thousands of people do something that sounds mad: they step out of a perfectly good aeroplane. Most of them land safely, and physics explains why.

As soon as a skydiver leaves the plane, two forces act on them. The first is their weight. This is the force acting on them because of gravity. It pulls them down towards the Earth. The second is air resistance. This is a type of friction that acts against their motion.

How heavy is a skydiver?

Weight depends on mass and on the gravitational field strength, g. Near the Earth’s surface, g is 9.8 N/kg. We use the equation W = m g.

Take a skydiver with a mass of 80 kg, including the kit. Their weight is W = 80 × 9.8 = 784 N. This force stays the same for the whole jump.

Speeding up, then levelling off

At the very start, the skydiver is barely moving downwards. Air resistance is tiny. The resultant force is the single force that has the same effect as all the forces acting together. Here it is large and acts downwards, so the skydiver accelerates.

Newton’s Second Law tells us how big the acceleration is: F = m a. Suppose that a few seconds into the fall, air resistance has grown to 500 N. The resultant force is 784 − 500 = 284 N downwards. The acceleration is a = F ÷ m = 284 ÷ 80 = 3.55 m/s². The skydiver is still speeding up, but more slowly than before.

Air resistance gets bigger as speed increases. Eventually it becomes equal to the weight. Now the resultant force is zero. Newton’s First Law says that if the resultant force on a moving object is zero, it carries on at the same speed in the same direction. The skydiver has reached terminal velocity. Lying belly-down, this is usually around 50–60 m/s. That is faster than a car on a motorway.

Opening the parachute

At about a kilometre above the ground, the skydiver pulls a cord. The parachute opens, and its huge surface area pushes against a lot more air. Suddenly air resistance is much bigger than the weight. The resultant force now acts upwards, so the skydiver decelerates. It feels like being yanked upwards, but they are still falling, just more slowly.

As they slow down, air resistance gets smaller. Soon it balances the weight again. The skydiver reaches a new, much lower terminal velocity of about 5 m/s. That is slow enough to land on their feet.

The story in a graph

A velocity–time graph shows the whole jump. The line starts at zero and rises steeply. It then curves and flattens out, because the acceleration gets smaller. The flat part is the first terminal velocity. When the parachute opens, the line drops sharply. Then it curves and flattens again at the lower terminal velocity. The gradient of the line at any point gives the acceleration. A flat line means zero acceleration and balanced forces.

Key words

• Weight: the force acting on an object due to gravity; measured in newtons (N).
• Gravitational field strength (g): the weight of each kilogram of mass; about 9.8 N/kg near the Earth’s surface.
• Resultant force: a single force that has the same effect as all the original forces acting together.
• Air resistance: a frictional force that acts against an object moving through air.
• Terminal velocity: the steady velocity reached by a falling object when the resultant force on it is zero.
• Newton’s First Law: if the resultant force on an object is zero, a stationary object stays still and a moving object keeps moving at the same speed in the same direction.
• Newton’s Second Law: the acceleration of an object is directly proportional to the resultant force on it and inversely proportional to its mass (F = m a).

Questions

1. What name is given to the steady speed a falling object reaches when the forces on it are balanced? [1 mark]
2. Name the two forces acting on a skydiver as they fall. [2 marks]
3. What happens to the size of the air resistance on the skydiver as their speed increases? [1 mark]
4. Explain why the skydiver slows down when the parachute opens. [3 marks]
5. Use Newton’s First Law to explain why a skydiver at terminal velocity does not speed up or slow down. [2 marks]
6. A skydiver has a mass of 65 kg. Gravitational field strength = 9.8 N/kg.
   a) Calculate the weight of the skydiver. Give the unit. [2 marks]
   b) At one moment the air resistance on the skydiver is 237 N. Calculate the resultant force on the skydiver and give its direction. [2 marks]
7. A skydiver and their equipment have a total mass of 90 kg. Just after the parachute opens, the resultant force on them is 1350 N upwards. Calculate the acceleration of the skydiver. Give the unit and the direction. [3 marks]
8. Describe the motion of a skydiver from the moment they leave the plane until they land. Explain the motion in terms of the forces acting, and describe the shape of the velocity–time graph. [6 marks]

Show answers

1. Terminal velocity (1)
2. Weight (1); air resistance / drag (1)
3. It increases / gets bigger (1)
4. The parachute has a much larger surface area, so air resistance increases (1); air resistance becomes greater than weight (1); so the resultant force acts upwards / opposite to the motion, so the skydiver decelerates (1)
5. Air resistance is equal to weight, so the resultant force is zero (1); so the skydiver continues at the same speed in the same direction / acceleration is zero (1)
6. a) W = 65 × 9.8 (1); W = 637 N (1)
   b) 637 − 237 (1); 400 N downwards (1) (allow error carried forward from part a)
7. a = F ÷ m or 1350 = 90 × a (1); a = 1350 ÷ 90 = 15 (1); 15 m/s² upwards (unit and direction both needed) (1)
8. Indicative content: at the start, speed is low so air resistance is small; weight is greater than air resistance, so resultant force is downwards and the skydiver accelerates; as speed increases, air resistance increases, so the resultant force and the acceleration decrease; eventually air resistance equals weight; resultant force is zero; skydiver reaches terminal velocity (constant speed); parachute opens; surface area increases, so air resistance increases and is greater than weight; resultant force acts upwards, so the skydiver decelerates; as speed falls, air resistance decreases until it equals weight again; a new, lower terminal velocity is reached; graph: steep line from zero that curves and levels off; sharp drop when the parachute opens; curves and levels off again at a lower velocity; gradient = acceleration.
   Level 3 (5–6 marks): a clear, logically ordered account of all stages of the jump, linking changes in air resistance and resultant force to the motion, with a correct description of the graph; Level 2 (3–4 marks): describes most stages with some correct links between forces and motion, may mention the graph; Level 1 (1–2 marks): simple statements about the motion or the forces with few or no links between them.

More reading: See all 30 GCSE Physics comprehension articles