(ENEM 2016) - QUESTÃO

Para um salto no Grand Canyon usando motos, dois paraquedistas vão utilizar uma moto cada, sendo que uma delas possui massa três vezes maior. Foram construídas duas pistas idênticas até a beira do precipício, de forma que no momento do salto as motos deixem a pista horizontalmente e ao mesmo tempo. No instante em que saltam, os paraquedistas abandonam suas motos e elas caem praticamente sem resistência do ar. 

As motos atingem o solo simultaneamente porque 

a) possuem a mesma inércia. 
b) estão sujeitas à mesma força resultante. 
c) têm a mesma quantidade de movimento inicial. 
d) adquirem a mesma aceleração durante a queda. 
e) são lançadas com a mesma velocidade horizontal.

_______________________________________________________________________ Resposta: D
Resolução Comentada:

O movimento descrito pelas motos é a composição de dois movimentos que ocorrem simultaneamente; na horizontal (movimento uniforme) e na vertical (queda livre), pois a única força que age em cada uma delas é seu próprio peso. Logo:
«math style=¨font-family:Tahoma¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mtable»«mtr»«mtd»«msub»«mi mathvariant=¨normal¨»R«/mi»«mi mathvariant=¨normal¨»A«/mi»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«msub»«mi mathvariant=¨normal¨»P«/mi»«mi mathvariant=¨normal¨»A«/mi»«/msub»«/mtd»«mtd/»«mtd/»«/mtr»«mtr»«mtd»«menclose notation=¨updiagonalstrike¨»«mi mathvariant=¨normal¨»m«/mi»«/menclose»«mfenced open=¨|¨ close=¨|¨»«msub»«mi mathvariant=¨normal¨»a«/mi»«mi mathvariant=¨normal¨»A«/mi»«/msub»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«menclose notation=¨updiagonalstrike¨»«mi mathvariant=¨normal¨»m«/mi»«/menclose»«mi mathvariant=¨normal¨»g«/mi»«/mtd»«mtd/»«mtd/»«/mtr»«mtr»«mtd»«mfenced open=¨|¨ close=¨|¨»«msub»«mi mathvariant=¨normal¨»a«/mi»«mi mathvariant=¨normal¨»A«/mi»«/msub»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi mathvariant=¨normal¨»g«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»cte«/mi»«/mtd»«/mtr»«/mtable»«mspace linebreak=¨newline¨/»«/mstyle»«/math»     «math style=¨font-family:Tahoma¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mtable»«mtr»«mtd»«msub»«mi mathvariant=¨normal¨»R«/mi»«mi mathvariant=¨normal¨»B«/mi»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«msub»«mi mathvariant=¨normal¨»P«/mi»«mi mathvariant=¨normal¨»B«/mi»«/msub»«/mtd»«mtd/»«/mtr»«mtr»«mtd»«menclose notation=¨updiagonalstrike¨»«mn»3«/mn»«mi mathvariant=¨normal¨»m«/mi»«/menclose»«mfenced open=¨|¨ close=¨|¨»«msub»«mi mathvariant=¨normal¨»a«/mi»«mi mathvariant=¨normal¨»B«/mi»«/msub»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«menclose notation=¨updiagonalstrike¨»«mn»3«/mn»«mi mathvariant=¨normal¨»m«/mi»«/menclose»«mi mathvariant=¨normal¨»g«/mi»«/mtd»«mtd/»«/mtr»«mtr»«mtd»«mfenced open=¨|¨ close=¨|¨»«msub»«mi mathvariant=¨normal¨»a«/mi»«mi mathvariant=¨normal¨»A«/mi»«/msub»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi mathvariant=¨normal¨»g«/mi»«/mtd»«mtd»«mo»=«/mo»«mo»§#xA0;«/mo»«mi»cte«/mi»«/mtd»«/mtr»«/mtable»«/mstyle»«/math»
Como as motos perderam o contato com as pistas (que possuem mesma altura) no mesmo instante, e na vertical o movimento é uniformemente acelerado (queda livre), podemos calcular o tempo de queda de cada uma delas:
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Assim, o tempo de queda das motos é o mesmo, independente de suas massas e de suas velocidades horizontais.