Temat 3: Throwing, jumping and shooting

The kinematic description of motion is useful for answering a whole range of questions.
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What is the upper limit for the long jump? The running peak speed world record in 2008 was over Ref. 59 12.5m/s ≈ 45 km/h by Usain Bolt, and the 1997 women’s record was 11m/s ≈ 40 km/h. However, male long jumpers never run much faster than about 9.5m/s. How much extra jump distance could they achieve if they could run full speed? How could they achieve that? In addition, long jumpers take off at angles of about 20°, as they are not able to achieve a higher angle at the speed they are running. How much would they gain if they could achieve 45°?
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What do the athletes Usain Bolt and Michael Johnson, the last two world record holders on the 200m race at time of this writing, have in common?They were tall, athletic, and had many fast twitch fibres in the muscles.These properties made them good sprinters. A last differencemade them world class sprinters: they had a flattened spine, with almost no S-shape.This abnormal condition saves them a little bit of time at every step, because their spine is not as flexible as in usual people. This allows them to excel at short distance races.
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Athletes continuously improve speed records. Racing horses do not. Why? For racing horses, breathing rhythm is related to gait; for humans, it is not. As a result, racing horses cannot change or improve their technique, and the speed of racing horses is essentially the same since it is measured.
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How can the speed of falling rain be measured using an umbrella?The answer is important: the same method can also be used to measure the speed of light, as we will find out later. (Can you guess how?) When a dancer jumps in the air, how many times can he or she rotate around his or her vertical axis before arriving back on earth?
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Numerous species of moth and butterfly caterpillars shoot away their frass – to put it more crudely: their shit – so that its smell does not help predators to locate them. Stanley Caveney and his team took photographs of this process. Figure 46 shows a caterpillar (yellow) of the skipper Calpodes ethlius inside a rolled up green leaf caught in the act. Given that the record distance observed is 1.5m (though by another species, Epargyreus clarus), what is the ejection speed? How do caterpillars achieve it?
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What is the horizontal distance one can reach by throwing a stone, given the speed and the angle from the horizontal at which it is thrown?
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What is the maximum numbers of balls that could be juggled at the same time?
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Is it true that rain drops would kill if it weren’t for the air resistance of the atmosphere? What about hail?
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Are bullets, fired into the air from a gun, dangerous when they fall back down?
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Police finds a dead human body at the bottom of cliff with a height of 30m, at a distance of 12m from the cliff. Was it suicide or murder?
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All land animals, regardless of their size, achieve jumping heights of at most 2.2m, as shown in Figure 47.The explanation of this fact takes only two lines. Can you find it? The last two issues arise because the equation (6) describing free fall does not hold in all cases. For example, leaves or potato crisps do not follow it. As Galileo already knew, this is a consequence of air resistance; we will discuss it shortly. Because of air resistance, the path of a stone is not a parabola. In fact, there are other situations where the path of a falling stone is not a parabola, even without air resistance. Can you find one?