Can anyone explain how I solve this? I\'ve tried but just cannot figure it out.

Question

Can anyone explain how I solve this? I've tried but just cannot figure it out. A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.2 m/s at ground level. The engines then fire, and the rocket accelerates upward at 4.20 m/s2 until it reaches an altitude of 1030 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of ?9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately.) (a) For what time interval is the rocket in motion above the ground? (b) What is its maximum altitude? (c) What is its velocity just before it hits the ground?

Explanation / Answer

a) s= 79.2 t+ 4.20 t^2/2 =1030 t1= 10.23 time for free fall s= + 1/ 9.8 t ^2/2 = 1030 t2= 14.49 total time = 24.72 s b) 1030 c) v= (2 a s +u^2)^0.5 a= g =9.8 s=1030 u=0 so v=142.08 m/s

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