A model rocket is launched straight upward with an initialspeed of 54.0 m/s. It

Question

A model rocket is launched straight upward with an initialspeed of 54.0 m/s. It accelerates with a constant upwardacceleration of 2.12 m/s2 until its engines stop at an altitude of150 m. Note: use g = 9.81 m/s2 in this problem. Hint: again treat thedifferent types of motion separately: (1) accelerating up (2)moving up with decreasing speed due to gravity (3) fallingdown. a)What is the maximum height reached by the rocket? Answer inunits of m. b) When does the rocket reach maximum height? Answer in unitsof s. c) How long is the rocket in the air? Answer in units ofs. Note: use g = 9.81 m/s2 in this problem. Hint: again treat thedifferent types of motion separately: (1) accelerating up (2)moving up with decreasing speed due to gravity (3) fallingdown. a)What is the maximum height reached by the rocket? Answer inunits of m. b) When does the rocket reach maximum height? Answer in unitsof s. c) How long is the rocket in the air? Answer in units ofs. c) How long is the rocket in the air? Answer in units ofs.

Explanation / Answer

Initial speed v = 54 m / s Accleration a = 2.12 m / s ^ 2 Altitude h = 150 m Speed at height h be V then from the relation V ^ 2 - v ^ 2 = 2ah                                           V = [ v ^ 2 + 2ah ]                                              = 59.59 m / s height reached by rocket above height h is h ' = V ^ 2 /2g                                                                     = 181.22 m So. Maximum height reached by the rocket from the ground H = h + h '                                                                                               = 331.22 m (b). timetaken to reach the height h is t = ( V - v ) /a                                                            =2.636 s time taken to reach H from height h is t ' = V /g                                                               = 6.08 s So, total time to reach height H from ground T = t + t'                                                                       = 8.716 s (c). time taken to reach the ground from height H is t " = [2H / g ]                                                                                    = 8.221 s So. total time in air = t + t ' + t "                               =16.93 s

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