A model rocket blasts off and moves upward with anacceleration of 12m/s^2 until

Question

A model rocket blasts off and moves upward with anacceleration of 12m/s^2 until it reaches a height of 27m, at whichpoint its engine shuts off and it continues it flight in freefall. A) what is the max height attained by the rocket? B)What is the speed of the rocket just before it hits theground? C)What is the total duration of the rockets flight? A model rocket blasts off and moves upward with anacceleration of 12m/s^2 until it reaches a height of 27m, at whichpoint its engine shuts off and it continues it flight in freefall. A) what is the max height attained by the rocket? B)What is the speed of the rocket just before it hits theground? C)What is the total duration of the rockets flight?

Explanation / Answer

Initial velocity u = 0 accleration a = 12 m / s ^ 2 height h = 27 m from the relation v^2 - u^2 = 2ah speed at 27 m is v = [ 2ah ] since u =0                              = 25.45 m / s (A). maximum height attained by rocket H = h + h ' where h ' = v ^ 2 / 2g                = 33.06 So, H = 60.06 m (B). In fall down condition : ----------------------------- Initial velocity U = 0 height H = 60.06 m accleration a = g = 9.8 m / s ^ 2 from the relation V ^ 2 - U^2 = 2gH                         V = [ 2gH ]                             = 34.31 m / s (c). time taken to ereach height h is t = ( v - u ) /a                                                        = 2.12 s time taken to travel h ' height t ' = v / g                                                 = 2.596 s time taken to fall on ground t " = [ 2H / g]                                                = 3.5s SO, total time = t + t ' + t "                      = 8.217 s

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