1. The problem statement, all variables and given/known data A 10.1 kg weather rocket generates a thrust of 193.0 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 415.0 N/m, is anchored to the ground. (a) Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed? (b) After the engine is ignited, what is the rocket's speed when the spring has stretched 12.5 cm past its natural length? (c)What would be the rockets speed after travelling the distance if it weren't tied down to the spring? 2. Relevant equations Usp= 1/2*k*x^2 3. The attempt at a solution I'm not too sure how to even begin thinking about this question. For (a) Am I right in the assumption that the weight of the rocket is directly related to the compression of the spring, thus the gravitational potential energy of the rocket should be equal to the spring energy? I tried mgh=1/2kx^2, where h=x. From this I got x=2(mg)/k, which is not the right answer. How would I break down this question? Any help is appreciated!