(Solved): KE: Kinetic Energy; \( \mathrm{KE}=11^{*} \) mass \( { }^{*} \) velocity \( { }^{2} \) [velocity \( ...

KE: Kinetic Energy; \( \mathrm{KE}=11^{*} \) mass \( { }^{*} \) velocity \( { }^{2} \) [velocity \( = \) speed] Law of Conservation of Energy: in a given system, energy cannot be created or destroyed. It can be transferred from one form to another, or transformed. 1 Newton \( (\mathrm{N})=1 \mathrm{~kg}^{*} 1 \mathrm{~m} / \mathrm{s}^{2}=1 \mathrm{kgm} / \mathrm{s}^{2} \) 1 Joule \( =1 N^{*} \) meter \( =1 \mathrm{kgm}^{2} / \mathrm{s}^{2} \) Problem 1. An amusement park owner is developing a new ride.. The coaster's track begins with a \( 320 \mathrm{~kg} \) cart starting from rest and rolling 34 meters down a incline (see diagram below). The cart then moves up a \( 21 \mathrm{~m} \) tall ramp. Assume that no energy is lost to heat or dissipated by friction or air resistance. How fast will the cart be going when it reaches the top of the \( 21 \mathrm{~m} \) tall ramp? Pick your answers: \[ \begin{array}{l} 5 \mathrm{~m} / \mathrm{s} \\ 12 \mathrm{~m} / \mathrm{s} \\ 8.8 \mathrm{~m} / \mathrm{s} \\ 16 \mathrm{~m} / \mathrm{s} \end{array} \] Show how you calculated the answer: