Drop an egg from 2 metres. Don't break it.

Step 1. How long does a 2 m drop take?

Rule: distance fallen = 5 × time × time (in metres and seconds). (From d = ½gt² with g ≈ 10 m/s²; ignores air resistance.)

2 m sits between 0.6 s and 0.7 s. Working backwards: time × time = 2 ÷ 5 = 0.4, so time = √0.4 ≈ 0.63 s. Check: 5 × 0.63 × 0.63 = 1.98 m. That's quick: about the time it takes to blink twice.

Step 2. How fast is it going when it lands?

Rule: speed gained = 10 × time. (v = gt.) 10 × 0.63 ≈ 6.3 m/s. In km/h: 6.3 × 3.6 ≈ 23 km/h, about as fast as a cyclist. Its average speed on the way down is only half that: 2 m ÷ 0.63 s ≈ 3.2 m/s.

Step 3. Drop, throw at an angle, or roll?

• Drop: falls 2 m, lands at 6.3 m/s, straight down.
• Throw sideways at 3 m/s: it still takes 0.63 s to fall 2 m (sideways speed doesn't change the fall), but it lands faster: √(3² + 6.3²) ≈ 7 m/s. Harder to protect. (Vertical and horizontal motion are independent; speeds combine by Pythagoras, M9-08-1.)
• Throw for distance: on flat ground, a throw at about 45° goes furthest (a bit less than 45° when you throw from a height). Measure it with a protractor. (Ignoring air resistance.)
• Roll down a ramp 2 m high: it reaches about the same speed at the bottom (a little less, because of friction), but it's moving along the floor, so you can stop it over a long distance. (Same height, same energy, Energy stores and transfers.)
• The big idea: for the same height, the egg ends up with about the same energy. What you control is how far, and how long, you take to stop it.

Step 4. Why cushions work: stopping distance and force

The egg has a mass of about 60 g = 0.06 kg, so it weighs 0.06 × 10 = 0.6 N. Dropped from 2 m, it gains 0.6 N × 2 m = 1.2 joules of movement energy. (Energy = weight × height, mgh.)

To stop it, the cushion pushes back over the distance it squashes. Rule: average stopping force ≈ energy ÷ stopping distance. (Work done = force × distance; we leave out the egg's own 0.6 N weight, which adds a little.)

Stopping time = stopping distance ÷ average speed while stopping (half the landing speed, 6.3 ÷ 2 ≈ 3.2 m/s). Check one row with force = mass × change in speed ÷ time: 0.06 × 6.3 ÷ 0.016 ≈ 24 N.

Ten times the stopping distance gives a tenth of the force: that's inverse proportion (M9-07-1). A hen's egg cracks at roughly a few tens of newtons pushed on its ends, and less on its side. It varies a lot from egg to egg, which is why you test.

Step 5. Spread the force

Pressure = force ÷ area. (p = F/A, Pressure in solids, liquids and gases.) 24 N pressing on a point of 1 cm² is 24 N per cm². A cradle that touches 10 cm² of shell spreads it to 2.4 N per cm². Same force, a tenth of the pressure. So hold the egg in a snug cup, not on a point.

Step 6. Slow the fall with drag

A parachute adds air resistance (Friction, air and water resistance). Time the drop with and without it.

Example numbers: yours will differ. Average speed = distance ÷ time (M8-08-2).

Step 7. Test your materials fairly

Squash test: stack the material 5 cm high in a paper cup, rest a 500 g bag of rice on it, and measure the new height. Do it three times and take the mean (M6-14-2). Squash % = (5 − new height) ÷ 5 × 100.

Example numbers, to show the method. What to look for: a good cushion squashes a long way (a long stopping distance) without squashing flat. If it bottoms out, the egg hits whatever is underneath. Fair test: same height, same weight, same cup, one material changed at a time (Fair tests and variables).