Jason launches a model rocket with a mass of 2.0 kg from his spring-powered rocket launcher with a spring constant of 800 N/m. He pulls it back .55 m. If Jason aims it straight up, what potential energy will the rocket have when it reaches its maximum height? What height will it reach?
Through conservation of mechanical energy, we know that the spring potential energy of the launcher will equal the gravitational potential energy of the rocket at the peak of its flight. Thus SPE = GPE = 1/2 kx2 = mgh. We know that k = 800, m = 2.0, x = .55.
Thus, we can plug these numbers into the equation and get
GPE = 1/2 (800) (.55) 2 = 121J. For height, we know the formula for gravitational potential energy is GPE = mgh.
Thus, we can plug in the values m = 2.0, and g ≈ 9.81 to solve for h.
We get 121 = (2.0) (9.81) h, h = 121/ (2.0) (9.81) = 6.17m