Please help A test rocket is fired vertically upward from a missile well sothat

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A test rocket is fired vertically upward from a missile well sothat it has velocity of 100 m/s when it is at ground level.the rocket accelerates upward at 4.00 m/s^2 untill it reaches analtitude of 1000m. at that point its engines fail and the remainderof the journey is in free "fall". a) once out of the well, for how long is the rocket flyingbefore the engines fail? b) How high is the rocket above the ground when the enginesfail? c) what is the rocket's maximum altitude above groundlevel? d) what is the rockets velocity just before it strikes theground? e) how long is the rocket above the ground before itcrashes? Please help

A test rocket is fired vertically upward from a missile well sothat it has velocity of 100 m/s when it is at ground level.the rocket accelerates upward at 4.00 m/s^2 untill it reaches analtitude of 1000m. at that point its engines fail and the remainderof the journey is in free "fall". a) once out of the well, for how long is the rocket flyingbefore the engines fail? b) How high is the rocket above the ground when the enginesfail? c) what is the rocket's maximum altitude above groundlevel? d) what is the rockets velocity just before it strikes theground? e) how long is the rocket above the ground before itcrashes?

Explanation / Answer

       The accelaration is a =4.00 m/s2        The height reached by therocket before engine fials is H = 1000 m   ------------------------------------------------------------------------------------ (a) now we find time taken to reach the heightH               From the equation of motion V2 -U2= 2as                                                             V2 -U2= - 2gH                                                                    V = ( U2 -2gH  )1/2                                                                        =---------- m/s       Then the time takenis  t1 = ( U -V ) / g                                                 = ------ sec (b) the hight of the rocket above the ground whenthe engines fails is H = 1000m    (c) The height reached by the rocket after engine failsis h = V2 /2g                                                                                         =-------- m          Then the total height reachedby the rocket is H + h = --------- m (d) The velocity of the rocket just before reach theground from the equation of motion is                        Vf2- Uh2 = 2as      where Uh = 0 is the veloctiy of therocket at the maximum height (H+h)                       Vf2- 0 = 2g(H+h)                              Vf = 2g(H+h)                            =-------- m/s     (e) time taken to reach the ground is t = time taken toreach the height H + time taken to reach the maximumheight                                                             time taken to reach the ground from the maximum height                                                          = t1 + V/g + Vf / g                                                           =--------- sec        The height reached by therocket before engine fials is H = 1000 m   ------------------------------------------------------------------------------------ (a) now we find time taken to reach the heightH               From the equation of motion V2 -U2= 2as                                                             V2 -U2= - 2gH                                                                    V = ( U2 -2gH  )1/2                                                                        =---------- m/s       Then the time takenis  t1 = ( U -V ) / g                                                 = ------ sec (b) the hight of the rocket above the ground whenthe engines fails is H = 1000m    (c) The height reached by the rocket after engine failsis h = V2 /2g                                                                                         =-------- m          Then the total height reachedby the rocket is H + h = --------- m (d) The velocity of the rocket just before reach theground from the equation of motion is                        Vf2- Uh2 = 2as      where Uh = 0 is the veloctiy of therocket at the maximum height (H+h)                       Vf2- 0 = 2g(H+h)                              Vf = 2g(H+h)                            =-------- m/s     (e) time taken to reach the ground is t = time taken toreach the height H + time taken to reach the maximumheight                                                             time taken to reach the ground from the maximum height                                                          = t1 + V/g + Vf / g                                                           =--------- sec

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