This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Convert the speed of the pickup truck from km/h to m/s. Given speed of pickup truck, v_1 = 90 km/h. v_1 = 90 km/h × 1000 m1 km × 1 h3600 s v_1 = (90 × 1000)/(3600) m/s v_1 = 25 m/s Step 2: Calculate the kinetic energy of the pickup truck. Given mass of pickup truck, m_1 = 2000 kg. The formula for kinetic energy is KE = (1)/(2)mv^2. KE_1 = (1)/(2)m_1 v_1^2 KE_1 = (1)/(2)(2000 kg)(25 m/s)^2 KE_1 = (1)/(2)(2000 kg)(625 m^2/s^2) KE_1 = 1000 × 625 J KE_1 = 625000 J Step 3: Set the kinetic energy of the sport car equal to the kinetic energy of the pickup truck. Given mass of sport car, m_2 = 1000 kg. We are given that KE_2 = KE_1. KE_2 = 625000 J Step 4: Solve for the speed of the sport car. Using the kinetic energy formula for the sport car: KE_2 = (1)/(2)m_2 v_2^2 625000 J = (1)/(2)(1000 kg)v_2^2 625000 = 500 v_2^2 v_2^2 = (625000)/(500) v_2^2 = 1250 v_2 = sqrt(1250) m/s v_2 ≈ 35.355 m/s Step 5: Convert the speed of the sport car back to km/h (optional, but often preferred for vehicle speeds). v_2 = 35.355 m/s × 3600 s1 h × 1 km1000 m v_2 = (35.355 × 3600)/(1000) km/h v_2 ≈ 127.278 km/h The speed of the sport car is approximately 35.4 m/s or 127.3 km/h. The speed of the sport car is 35.4 m/s.