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Movement, stability and measurement

Solution and notes

These notes discuss the trajectory of a projectile as observed by someone wanting to intercept it, the stability of aircraft (achieved by a combination of forces) and nuclei (related to nuclear binding energy), and early Chinese work on measurement

Imagine you are watching the flight of a ball through the air and that you have to hit it or catch it. It was once thought that the brain performed some amazing, and totally unconscious, calculations to do with the ball’s trajectory and where it would end up. We now know that this is not the case.

The simplest situation is when the catcher is at rest and in exactly the right place, i.e. if you were deliberately being thrown the ball. It will take a parabolic path and, as you watch it, the angle it appears to make with you will change. It turns out that for shallow trajectories this angle changes at a constant rate, making things fairly easy for the catcher (Box 1). This result is to be found in Len Fisher’s interesting book (see References and further reading). For large angles the change in angle with time is noticeably non-linear, which may explain why higher ball trajectories are harder to catch.

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