Final answer:
To maintain the same kinetic energy after a 30 kg suitcase falls off a car, the car, now weighing 250 kg, must travel at a slightly higher velocity than the initial 45 m/s. This is calculated using the kinetic energy formula KE = 0.5 * m * v^2.
Step-by-step explanation:
Calculating the Car's Velocity to Maintain Kinetic Energy After the Suitcase Falls Off
The question asks us to find the new velocity of a car when a suitcase falls off, so that the car maintains the same kinetic energy. Initially, the combined mass of the car and the suitcase is 280 kg, and they are moving at a velocity of 45 m/s. After a 30 kg suitcase falls off, we need to determine what velocity the 250 kg car must have to keep its kinetic energy the same.
Kinetic energy is given by the equation KE = 0.5 * m * v^2. The initial kinetic energy with both the car and the suitcase can be calculated using KE = 0.5 * 280 kg * (45 m/s)^2. To maintain this kinetic energy after the suitcase falls off, we solve for the new velocity using the same kinetic energy value but with the new mass of the car alone. Therefore, we use the formula KE = 0.5 * 250 kg * v^2 and solve for v. After calculations, we would find that the car must travel at a slightly higher velocity than 45 m/s to maintain the same kinetic energy, since the total mass of the system has decreased.