This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the initial and final mechanical energies. The change in mechanical energy ( E_mech) is the sum of the change in kinetic energy ( K) and the change in potential energy ( U). When non-conservative forces like air resistance are present, the work done by these forces (W_nc) is equal to the change in mechanical energy. W_nc = E_mech = (K_f + U_f) - (K_i + U_i) Given: Mass of projectile, m = 12 kg Initial vertical speed, v_i = 20 m/s Maximum height reached, h_f = 18 m Acceleration due to gravity, g = 9.8 \, m/s^2 Step 2: Calculate the initial kinetic energy (K_i) and initial potential energy (U_i). At the launch point, we set the initial height h_i = 0. K_i = (1)/(2)mv_i^2 K_i = (1)/(2)(12 \, kg)(20 \, m/s)^2 K_i = 6 \, kg × 400 \, m^2/s^2 K_i = 2400 \, J U_i = mgh_i = (12 \, kg)(9.8 \, m/s^2)(0 \, m) U_i = 0 \, J Step 3: Calculate the final kinetic energy (K_f) and final potential energy (U_f). At the maximum height, the vertical speed of the projectile is momentarily zero, so v_f = 0. K_f = (1)/(2)mv_f^2 K_f = (1)/(2)(12 \, kg)(0 \, m/s)^2 K_f = 0 \, J The final height is h_f = 18 m. U_f = mgh_f U_f = (12 \, kg)(9.8 \, m/s^2)(18 \, m) U_f = 2116.8 \, J Step 4: Calculate the change in mechanical energy. E_mech = (K_f + U_f) - (K_i + U_i) E_mech = (0 \, J + 2116.8 \, J) - (2400 \, J + 0 \, J) E_mech = 2116.8 \, J - 2400 \, J E_mech = -283.2 \, J Step 5: Convert the result to kilojoules (kJ) and select the closest option. E_mech = -283.2 \, J × 1 \, kJ1000 \, J = -0.2832 \, kJ Rounding to two decimal places, this is -0.28 kJ. The final answer is a. -0.28 kJ. 3 done, 2 left today. You're making progress.