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Un corp cade liber de la inaltimea h=20m iar al doilea corp este lansat simultan pe verticala de la suprafata Pamantului . Se neglijeaza frecarea cu aerul. Stiind ca cele doua corpuri ajung simultan pe sol , sa se afle :
a. viteza initiala cu care se arunca corpul al doilea
b.inaltimea maxima atinsa de corpul al doilea
c. vitezele cu care sosesc corpurile la sol


Răspuns :

a) xā‚=h-vā‚€ā‚t-gtĀ²/2=h-gtĀ²/2

xā‚‚=vā‚€ā‚‚t-gtĀ²/2

xā‚=0=>h=gtĀ²/2<=>20=10tĀ²/2=>tĀ²=4=>t=Ā±āˆš4=Ā±2

t>0=>t=2 s

xā‚=xā‚‚=>h-gtĀ²/2=vā‚€ā‚‚t-gtĀ²/2=>vā‚€ā‚‚t=h=>vā‚€ā‚‚=h/t=20/2=10 m/s

b) vĀ²=vā‚€ā‚‚Ā²-2ghā‚‚<=>0Ā²=10Ā²-2*10hā‚‚<=>2hā‚‚=10=>hā‚‚=10/2=5 m

c) vā‚Ā²=vā‚€ā‚Ā²+2gh=0Ā²+2*10*20=400=>vā‚=Ā±āˆš400=Ā±20 m/s

vā‚>0=>vā‚=20 m/s

vā‚‚Ā²=vĀ²+2ghā‚‚=0Ā²+2*10*5=100=>vā‚‚=Ā±āˆš100=Ā±10 m/s

vā‚‚>0=>vā‚‚=10 m/s