1. The problem statement, all variables and given/known data During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 990 m above the earth's surface. The rocket's engines give the rocket an upward acceleration of 16.0 m/s2 during the time T that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance. What it asks for : What must be the value of T in order for the rocket to reach the required altitude? 2. Relevant equations basic kinematics formulas X= Xo + VoT+1/2AT^2 V=Vo+AT V^2=Vo^2+2A(X-Xo) o denotes initial 3. The attempt at a solution | X3= 990 V3=0 | | | X2= V2= A=-9.8 | | | | X1=0 V1=0 A=16.0 m/s X3=X2+V2T-1/2 9.8T^2 X2=X1+V1T+.5*16*T^2 X2=0+0T+.5^16*T^2 X2=8T^2 plugging pack into original equation: X3=8T^2 +V2T -4,9 T^2 combining like terms X3= 3.1T^2 + V2T finding V2: V2=V1+16T V2=0+16T V2=16T plugging back in X3= 3.1T^2 + 16T X3=990 990=3.1T^2 + 16T it is a quadratic equation I graphed it to find the X value, I got 20.65 , but it is wrong, where Did I go wrong?