Rakieta startuje z ziemi pionowo do góry ruchem jednostajnie przyspieszonym prostoliniowym z przyspieszeniem 20m/s[kwadrat]. W jakim czasie wzniesie się ona na wysokość 20km? Jaką prędkość uzyska?
Isoko
![Dane:\\a = 20 [ \frac{m}{s^2}]\\h = 20 km = 20 000[m ]\\\\Szukane :\\\Delta t = ? \\\Delta v = ? \\\\Rozwiazanie :\\h = \frac{1}{2}at^2 \\\Delta t = \sqrt{ \frac{h}{1/2a} } \\\\a = \frac{\Delta v}{\Delta t}\\\Delta v = \Delta t\cdot a \\\\\\\Delta t = \sqrt{ \frac{20000}{1/2\cdot 20} } = \sqrt{2000} = 44,7 [s]\\\\\Delta v = 44,7 \cdot 20 = 894 [\frac{m}{s}]](https://tex.z-dn.net/?f=Dane%3A%5C%5Ca+%3D+20+%5B+%5Cfrac%7Bm%7D%7Bs%5E2%7D%5D%5C%5Ch+%3D+20+km+%3D+20+000%5Bm+%5D%5C%5C%5C%5CSzukane+%3A%5C%5C%5CDelta+t+%3D+%3F+%5C%5C%5CDelta+v+%3D+%3F+%5C%5C%5C%5CRozwiazanie+%3A%5C%5Ch+%3D++%5Cfrac%7B1%7D%7B2%7Dat%5E2+%5C%5C%5CDelta+t+%3D++%5Csqrt%7B+%5Cfrac%7Bh%7D%7B1%2F2a%7D+%7D+%5C%5C%5C%5Ca+%3D++%5Cfrac%7B%5CDelta+v%7D%7B%5CDelta+t%7D%5C%5C%5CDelta+v+%3D+%5CDelta+t%5Ccdot+a+%5C%5C%5C%5C%5C%5C%5CDelta+t+%3D++%5Csqrt%7B+%5Cfrac%7B20000%7D%7B1%2F2%5Ccdot+20%7D+%7D+%3D++%5Csqrt%7B2000%7D+%3D+++44%2C7+%5Bs%5D%5C%5C%5C%5C%5CDelta+v+%3D+44%2C7+%5Ccdot+20+%3D+894++%5B%5Cfrac%7Bm%7D%7Bs%7D%5D+ "Dane:\\a = 20 [ \frac{m}{s^2}]\\h = 20 km = 20 000[m ]\\\\Szukane :\\\Delta t = ? \\\Delta v = ? \\\\Rozwiazanie :\\h = \frac{1}{2}at^2 \\\Delta t = \sqrt{ \frac{h}{1/2a} } \\\\a = \frac{\Delta v}{\Delta t}\\\Delta v = \Delta t\cdot a \\\\\\\Delta t = \sqrt{ \frac{20000}{1/2\cdot 20} } = \sqrt{2000} = 44,7 [s]\\\\\Delta v = 44,7 \cdot 20 = 894 [\frac{m}{s}]")
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