Your physical therapist throws a baseball to you at a certain speed and you catch it. To increase the difficulty, the therapist is going to throw you a medicine ball whose mass is ten times the mass of the baseball. You are given the following choices. Rank these from easiest to hardest to catch.
1. The medicine ball thrown at the same speed as the baseball
2. The medicine ball thrown with the same momentum as the baseball.
3. The medicine ball thrown with the same kinetic energy as the baseball.
To rank these choices from easiest to hardest to catch, we need to consider how different properties of the medicine ball affect its difficulty to catch compared to the baseball.
Here is the ranking from easiest to hardest:
1. The medicine ball thrown at the same speed as the baseball: This choice should be the easiest to catch because both balls have the same speed. Since the speed is the same, the medicine ball won't feel any different than the baseball in terms of how fast it is moving towards you. The mass difference won't have an impact on the difficulty of catching.
2. The medicine ball thrown with the same momentum as the baseball: This choice would be harder to catch compared to the previous one. Momentum depends on both mass and speed, so if the medicine ball has ten times the mass of the baseball, it would require the therapist to throw it with a lower speed to achieve the same momentum. The lower speed would give you less time to react and catch the ball, making it more difficult.
3. The medicine ball thrown with the same kinetic energy as the baseball: This choice would be the hardest to catch. Kinetic energy depends on the mass and the square of the speed. Since the medicine ball has ten times the mass of the baseball, it would require a much higher speed to have the same kinetic energy. The combination of higher mass and higher speed would make the medicine ball more difficult to catch, as it would be moving much faster and have more force behind it.
To rank these choices from easiest to hardest to catch, let's understand the concepts involved.
1. Speed: Speed is the rate at which an object covers a distance. In this case, if the medicine ball is thrown at the same speed as the baseball, catching it should be relatively similar in difficulty. The mass of the medicine ball being ten times that of the baseball may make it feel heavier, but the speed plays a more significant role in catchability.
2. Momentum: Momentum is the product of an object's mass and velocity. Since the medicine ball has ten times the mass of the baseball, to have the same momentum, it needs to be thrown with a lower velocity. Catching a medicine ball with the same momentum as the baseball would be more challenging than catching it with the same speed because the higher mass results in greater force upon impact.
3. Kinetic Energy: Kinetic energy is the energy possessed by an object due to its motion. It is proportional to the square of an object's velocity. Since the kinetic energy depends on both mass and velocity, to have the same kinetic energy as the baseball, the medicine ball needs to be thrown with a much higher velocity. Catching a medicine ball with the same kinetic energy as the baseball would be the most challenging because of the increased mass and velocity.
Based on this information, the ranking from easiest to hardest to catch would be as follows:
1. The medicine ball thrown at the same speed as the baseball.
2. The medicine ball thrown with the same momentum as the baseball.
3. The medicine ball thrown with the same kinetic energy as the baseball.