A model Rocket is launched straight upward with an initialvelocity of 54.7 m/s.

Question

A model Rocket is launched straight upward with an initialvelocity of 54.7 m/s. It's accelerates with a constant upwardacceleration of 1.74 m/s^2 until its engines stop at an altitude of233m.    What is the maximum height reached by the rocketin units of meters. How long after lift-off does the rocket reachits maximum height in units of seconds. A model Rocket is launched straight upward with an initialvelocity of 54.7 m/s. It's accelerates with a constant upwardacceleration of 1.74 m/s^2 until its engines stop at an altitude of233m.    What is the maximum height reached by the rocketin units of meters. How long after lift-off does the rocket reachits maximum height in units of seconds.

Explanation / Answer

   Let v be the velocity of the rocketwhen the engine stops.    Then v2 -(54.7m/s)2 = (2)(1.74m/s2)(233m)    Solving for v we get v =61.67m/s    Now from this point the rocket reaches adistance of v2/2g =(61.67m/s)2/[(2)(9.8m/s2)]                                                                                             = 194m    Therefore the height reached by the rocketis 233m + 194m = 427m    Now time to reach the point where the enginehas stopped is t = (61.67m/s - 54.7m/s)/(1.74m/s2)                                                                                                  =4s    From this point the time taken by the rocketto reach the maximum height is t =(61.67m/s)/(9.8m/s2)                                                                                                                       = 6.3s    Therefore the total time taken by the rocketto reach the maximum height is 4s + 6.3s = 10.3s

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