The six figures below depict six model rockets that have just had their engines

Question

The six figures below depict six model rockets that have just had their engines turned off. All of the rockets are aimed straight up, but their speeds differ. All of the rockets are the same size and shape, but they carry different loads, so their masses differ. The specific mass and speed for each rocket is given in each figure. (In this situation, we are going to ignore any effect air resistance may have on the rockets.) At the instant when the engines are turned off, the rockets are all at the same height. Rank these model rockets, from greatest to least, on the basis of the maximum height they will reach. Greatest 1 2 3 4 5 6 Least Or, all rockets reach the same height. Please carefully explain your reasoning. How sure were you of your ranking? (circle one) Basically Guessed Sure Very Sure 1 2 3 4 5 6 7 8 9 10 6 T. O'Kuma Ranking Task Exercises in Physics: Student Edition 6

Explanation / Answer

   K.E. ofrocket   =   (1/2) * m *v2    P.E. of rocket at maximumheight   =   m * g * h    According to law of conservation ofenergy    (1/2) * m *v2   =   m * g * h    maximum height reached byrocket      h   =   v2/ 2 * g    1.   v   =   30,   hA   =   302/ 2 *9.8   =   45.92   m    2.   v   =   40,   hB   =   402/ 2 *9.8   =   81.63   m    3.   v   =   20,   hC   =  202/ 2 *9.8   =   20.41   m    4.   v   =   20,   hD   =  202/ 2 *9.8   =   20.41   m    5.   v   =   40,   hE   =   402/ 2 *9.8   =   81.63   m    6.   v   =   20,   hF   =  202/ 2 *9.8   =   20.41   m    Clearly   hB   =   hE  >   hA  >   hC   =   hD   =   hF    P.E. of rocket at maximumheight   =   m * g * h    According to law of conservation ofenergy    (1/2) * m *v2   =   m * g * h    maximum height reached byrocket      h   =   v2/ 2 * g    1.   v   =   30,   hA   =   302/ 2 *9.8   =   45.92   m    2.   v   =   40,   hB   =   402/ 2 *9.8   =   81.63   m    3.   v   =   20,   hC   =  202/ 2 *9.8   =   20.41   m    4.   v   =   20,   hD   =  202/ 2 *9.8   =   20.41   m    5.   v   =   40,   hE   =   402/ 2 *9.8   =   81.63   m    6.   v   =   20,   hF   =  202/ 2 *9.8   =   20.41   m    Clearly   hB   =   hE  >   hA  >   hC   =   hD   =   hF

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