A test rocket is fired vertically upward from a well. Acatapult gives it an init

Question

A test rocket is fired vertically upward from a well. Acatapult gives it an initial speed of 80.0 m/s at ground level. Its engines then fireand it accelerates upward at 4.00m/s2 until it reaches an altitude of 1020 m. At that point its engines fail, and therocket goes into free fall, with an acceleration of -9.80m/s2. (You will need to consider the motion while theengine is operating separate from the free-fall motion.) (a) How long is the rocket in motion above theground?
(b) What is its maximum altitude?
(c) What is its velocity just before it collides with theEarth?
A test rocket is fired vertically upward from a well. Acatapult gives it an initial speed of 80.0 m/s at ground level. Its engines then fireand it accelerates upward at 4.00m/s2 until it reaches an altitude of 1020 m. At that point its engines fail, and therocket goes into free fall, with an acceleration of -9.80m/s2. (You will need to consider the motion while theengine is operating separate from the free-fall motion.) (a) How long is the rocket in motion above theground?
(b) What is its maximum altitude?
(c) What is its velocity just before it collides with theEarth?

Explanation / Answer

          Giventhat the initial speed is u = 80 m/s           Theaccelaration is a = 4 m/s2             Theheight reached by the rocket is h = 1020 m -------------------------------------------------------------   Final velocity of the rocket at height h is v2 - u2 = 2ah                                                                         v= (u2 +2ah )1/2                                                                            = -------- m/s Then the time taken to reach the height h is t1 =( v -u ) /a                                                                        =--------sec After engine fail             The height reached by the rocket is V2 -v2 = 2aH                                                                     0 -  v2 = -2gH                                                                               H=  v2 / 2g                                                                                = --------- m             Time taken is t2 =   ( V -v ) /a                                       =  ( 0-v ) /-g                                      =v /g                                     = ------- sec      Total time taken to reach the maximumheight is t = t1 + t2 (a) Total time of the rocket above the groumdis  T = 2t (b) The maximum altitude is H + h = --------m   (c)Apply equation of motion at the heightpoint , point where the rocket just before touch theground                                 V = U + gt                                   V= 0 + gt                                       =gt                                       =g(t1+t2)                                       =-------- m/s                                                                                                                                                                                  = -------- m/s Then the time taken to reach the height h is t1 =( v -u ) /a                                                                        =--------sec After engine fail             The height reached by the rocket is V2 -v2 = 2aH                                                                     0 -  v2 = -2gH                                                                               H=  v2 / 2g                                                                                = --------- m             Time taken is t2 =   ( V -v ) /a                                       =  ( 0-v ) /-g                                      =v /g                                     = ------- sec      Total time taken to reach the maximumheight is t = t1 + t2 (a) Total time of the rocket above the groumdis  T = 2t (b) The maximum altitude is H + h = --------m   (c)Apply equation of motion at the heightpoint , point where the rocket just before touch theground                                 V = U + gt                                   V= 0 + gt                                       =gt                                       =g(t1+t2)                                       =-------- m/s                                                                                                                                                                           0 -  v2 = -2gH                                                                               H=  v2 / 2g                                                                                = --------- m             Time taken is t2 =   ( V -v ) /a                                       =  ( 0-v ) /-g                                      =v /g                                     = ------- sec      Total time taken to reach the maximumheight is t = t1 + t2 (a) Total time of the rocket above the groumdis  T = 2t (b) The maximum altitude is H + h = --------m   (c)Apply equation of motion at the heightpoint , point where the rocket just before touch theground                                 V = U + gt                                   V= 0 + gt                                       =gt                                       =g(t1+t2)                                       =-------- m/s                                                                                                      

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