In this problem we will consider the equations of motion in vertical direction as follows 1-) V = Vi + g t 2-) S = Vi + ½ gt2 3-) V2 = Vi + 2gS Where V is object velocity at any moment S is ths distance traveled for the period under invesitigation Vi is the velocity of the object at beginning of period under invisitigation t is the time that object consumed to travel in the period under invsitigation g is the gravity acceleration and it equals 9.8 m/s to answer this problem we will use equation No 3 in this case S = 100-H where H is the height at which engine will be cut to achive 100 m exactly V = 0 velocity of the rocket should reach 0 at 100 m height That leads to equation 3 to be Vi=2g (100-H) by substitute the 3 senarios mentioned in the quistion in this final equation we will find out that senario (a) is the right answer