1. The problem statement, all variables and given/known data A 1Kg rocket is fired off. The engine provides a thrust of 18 Newtons for 20 meters. What is the maximum height achieved by the rocket? Assume no loss of mass and no friction. Gravity=9.8m/s^2 2. Relevant equations Work=Force x distance Force=Mass x acceleration(or gravity) Potential gravitational energy(PE)=Mass x Gravity x Height Kinetic energy(KE)=(1/2) x Mass x Velocity^2 I have a disagreement with my teacher on how to correctly solve this type of problem. Both of us agree that I need to find the work done by the engine of the rocket during the first 20 meters of flight first (W= 18N*20m=360 joules). After this is where my teacher and I begin to differ. My teacher says that I need to then set the work done by the engine = to the maximum PE of the rocket and solve for the height(W=PE so maximum height= W of engine / (Mass x Gravity) = 360/(1*9.8)= 36.7 joules). I believe that in this solution energy is not conserved. From what I understand, since the rocket only stops accelerating at 20 meters, the work of the engine up to this point should be set = to its KE. This gives you a KE 360 joules. The rockets PE, if measured from the highest point of its flight down to 20 meters, is 360 joules. This value does not account for the 20 meters before the rocket begins to be decelerate from gravity when it is still accelerating therefore you must find the PE of the rocket at 20 meters (9.8m/s^2 * 20m * 1Kg = 196 joules) and add that onto the KE at 20 meters in order to have the maximum PE for the rocket (556 joules) since it will convert that KE into PE in a 1:1 rate. Using this value for PE you get a maximum of 56.7 meters. Which of us is right with this? Is my logic sound in this matter?