Baseball and medicine ball thrown with different KE/P/V

[bdh2991]

Homework Statement

Your physical education teacher throws a baseball to you at
a certain speed and you catch it. The teacher is next going to throw you a
medicine ball whose mass is ten times the mass of the baseball. You are given
the following choices: You can have the medicine ball thrown with (a) the
same speed as the baseball, (b) the same momentum, or (c) the same kinetic
energy. Rank these choices from easiest to hardest to catch.

Homework Equations

p = mv
KE = 1/2 m v^2

The Attempt at a Solution

i originally thought it would be a, c, b, but i know that's wrong now and i don't know how i can derive the right answers mathematically with variables

 

[howie8594]

Think about that answer. If you catch something 10 times heavier going at the same speed, it's kinetic energy and its momentum are both going to be multiplied by 10. So given that you have a choice between the same momentum, the same kinetic energy, or 10 times as much momentum and kinetic energy, I'd say the choice "a" is by far the worst option.

In order to keep the same momentum and kinetic energy for the heavier ball, it's speed would have to be reduced, so b and c would make much more sense.

 

[bdh2991]

ok i understand how a is the worst but how would you be able to tell out of b and c is easier/harder?

 

[howie8594]

I recommend plugging in some numbers to both formulas, say... .5 kg for the baseball and 5 kg for the medicine ball. Then make up a velocity for the baseball to be going. Solve for momentum and kinetic energy. Once you get momentum in kgm/s and kinetic energy in joules, then plug those in for the medicine ball with 10 times as much mass, and solve for the velocity the medicine ball would have to be going for the momentum/KE to be the same.

 

[Nickie]

I would like to clarify that the choices given in this scenario are not directly related to the concepts of kinetic energy, momentum, and velocity. The difficulty in catching an object is not solely determined by its KE/P/V, but also by other factors such as the object's size, shape, and surface texture, as well as the catcher's skill and reaction time.

However, if we consider only the choices given and assume that all other factors are constant, the easiest to catch would be option (a), where the medicine ball is thrown at the same speed as the baseball. This is because the catcher would only have to adjust their hands to the velocity of the ball and not the mass, making it easier to catch.

The second easiest option would be (b), where the medicine ball is thrown with the same momentum as the baseball. In this case, the catcher would have to adjust for the increased mass of the ball, but since momentum is dependent on both mass and velocity, the difference in velocity would not be as significant, making it easier to catch compared to option (c).

The hardest option to catch would be (c), where the medicine ball is thrown with the same kinetic energy as the baseball. This is because the catcher would have to adjust for the increased mass and velocity of the ball, making it more difficult to catch accurately.

In conclusion, the correct ranking of the choices from easiest to hardest to catch would be (a), (b), (c). However, it is important to note that in real-life scenarios, other factors would also play a significant role in determining the difficulty of catching an object.