(Solved): Problem 5 Relative motion An airplane is launched from an aircraft carrier that is travelling at c ...

Problem 5 Relative motion An airplane is launched from an aircraft carrier that is travelling at constant velocity of 15 \( \mathrm{m} \cdot \mathrm{s}^{-1} \). The runway of the aircraft carrier is directed in its direction of motion and the catapult used to accelerate the \( 4000 \mathrm{~kg} \) airplane applies a constant force over 3 seconds to bring the absolute velocity of the airplane to a speed of \( 80 \mathrm{~m} \cdot \mathrm{s}^{-1} \) that is necessary for the airplane to fly a) What is the force applied to the airplane by the catapult? ( \( 50 \% \) points) b) Determine the length of the runway. ( \( 50 \% \) points) c) Comment on the forces experienced by the pilot sitting in the airplane. ( \( 10 \% \) bonus points) Remember that \[ \begin{aligned} \int \sum \mathbf{F} \mathrm{d} t &=\Delta \mathbf{G}_{r e l} \\ \mathrm{~d} U_{r e l} &=\mathrm{d} T_{r e l} \end{aligned} \]