Question about the Kinetic Energy of a baseball in flight

[hidemi]

Homework Statement

How baseball move

Relevant Equations

Vx = V cosθ
Vy = V sinθ - 9.8t

A baseball is thrown and lands 120 m away. While the ball is in flight, assuming the effect of air friction is negligible, which of the following is true?

a. At maximum height the ball has its greatest kinetic energy.
b. The horizontal component of the baseball’s kinetic energy is constant.
c. The vertical component of the baseball’s kinetic energy is constant.
d. The mechanical energy of the baseball is greater when nearer to the ground.
e. No answer above is correct.

The correct is E.
-----------------------------

Explaination
The vertical component of the baseball will be increased by gravity, while the horizontal component stays the same. So, I think the answer should be B.
Where am I doing wrong?

 

[mjc123]

Kinetic energy is not a vector and does not have vertical and horizontal components.

 

[hidemi]

What I was trying to indicate from the equations above is that Vx is constant, so KEx=1/2m(Vx)^2 is constant throughout the flight. In contrast, Vy is affected by the gravity and thus is constantly changing, so does its KEy.

 

[PeroK]

Kinetic energy is not a vector and does not have vertical and horizontal components.

It's a poor question as answer b is technically wrong but physically/semantically correct: the contribution to the kinetic energy from the horizontal component of velocity is constant. I'm not sure that there is a name for $\frac 1 2 mv_x^2$, but whatever name we give it, it is a constant of the motion.

You might say "the $x$ component of kinetic energy" is as good a name as any! The term component is not exclusive to vectors.

 

[kuruman]

It's a poor question as answer b is technically wrong but physically/semantically correct: the contribution to the kinetic energy from the horizontal component of velocity is constant. I'm not sure that there is a name for $\frac 1 2 mv_x^2$, but whatever name we give it, it is a constant of the motion.

You might say "the $x$ component of kinetic energy" is as good a name as any! The term component is not exclusive to vectors.

Yet OP says the correct answer is E, "No answer above is correct." This means that the author of the question considers answer B incorrect and limits the term "component" to vectors, perhaps to make the point that, although v_x deserves the name component, v_x² does not.

On edit: The danger of accepting the name "component" for ½mv_x² and ½mv_y² is that, to get the "magnitude" K, we simply add the components thus blessing, instead of excoriating, the often-seen novice error of merely adding horizontal and vertical components of "real" vectors to get the magnitude of the resultant.

 

[haruspex]

Yet OP says the correct answer is E, "No answer above is correct." This means that the author of the question considers answer B incorrect and limits the term "component" to vectors, perhaps to make the point that, although v_x deserves the name component, v_x² does not.

On edit: The danger of accepting the name "component" for ½mv_x² and ½mv_y² is that, to get the "magnitude" K, we simply add the components thus blessing, instead of excoriating, the often-seen novice error of merely adding horizontal and vertical components of "real" vectors to get the magnitude of the resultant.

I beg to differ. We are so used to using the noun 'component' to refer to vectors that we forget that it can equally be used for scalar and even non-numeric entities. I see no serious objection to using a component of KE to mean that part of the KE associated with the body's motion in a certain direction.
Of course, how components should be combined to a whole depends on their nature. Even for vectors it is not simply a matter of performing vector addition: that only works if the given components are mutually orthogonal.

 

[hidemi]

Thank you all for making great points about the wording of the options.
I would still like to confirm regardless the word 'component,' is B still a correct answer because horizontal speed is not affected by any other factors and thus the horizontal kinetic energy remains constant throughout? Thanks!

 

[haruspex]

Thank you all for making great points about the wording of the options.
I would still like to confirm regardless the word 'component,' is B still a correct answer because horizontal speed is not affected by any other factors and thus the horizontal kinetic energy remains constant throughout? Thanks!

It's correct if you allow the notion of KE having components associated with different directions. I do.

 

[kuruman]

Thank you all for making great points about the wording of the options.
I would still like to confirm regardless the word 'component,' is B still a correct answer because horizontal speed is not affected by any other factors and thus the horizontal kinetic energy remains constant throughout? Thanks!

We all agree that ½mv_x² is a constant of the motion.

If you said that the given correct answer is B, I would go along with it because I accept the reasoning by @PeroK in #4 and @haruspex in #6. For reasons I outlined in #5, my personal preference is to avoid using "component" for kinetic energy and use instead other locutions to describe the same idea. If I were to write this question, I would use ½mv_x² and ½mv_y² in which case the correct answer would be clearly B and not E.

You actually said that the answer given as correct is E. When one accepts E as correct, one logically rejects B because it is "one of the above". Rejecting B also rejects the notion that the word "component" can be associated with kinetic energy since one knows that ½mv_x² is a constant of the motion. I can accept this point of view and go along with it divining that the author wanted to test whether you understand that kinetic energy is not a vector. Thus, I cannot confirm that B can be considered correct regardless of the word component.

Is it a poor question as @PeroK suggests in #4? I think an apter description might be "controversial" because of the discussion it stirred among us. In cases of poorly written or ambiguous multiple choice questions, the intent of the author can be deduced if the "correct" answer is given. This is one such case and I have already expressed my opinion about the author's intent.

Is it possible that

The correct is E.

is a typo somewhere down the line when "The correct is B" was the intention of solution writer? It is. I can go along with that too.