Final answer:
You should choose to catch the bowling ball with the same momentum as the basketball, because it will be moving slower due to its greater mass, making it safer and easier to catch compared to one with the same kinetic energy.
Step-by-step explanation:
If you catch a basketball and then are challenged to catch a bowling ball with either the same kinetic energy or the same momentum as the basketball, the best choice would be to catch the bowling ball with the same momentum. Momentum is defined as the product of mass and velocity (momentum = mass × velocity), and in the context of catching objects, a bowling ball with the same momentum as a basketball will typically be moving slower due to its greater mass. This is because, for a given momentum, a more massive object will have a proportionally lower velocity.
To understand this practically: suppose that a basketball is moving with a certain momentum. If a bowling ball has the same momentum, it means the product of its mass and velocity is the same as that of the basketball. Since the bowling ball has a greater mass, it must have a lower velocity in order to maintain the same momentum. This lower velocity would make it safer and easier to catch compared to one with the same kinetic energy.
The concept of kinetic energy, which is given by the formula KE = (1/2) × mass × velocity2, implies that, for the same kinetic energy, the bowling ball would have a surprisingly high velocity because it has a larger mass requiring a higher velocity to have the same kinetic energy as the basketball. This could be dangerous and more difficult to catch.