What is faster the cannon ball or its shadow?

[Liam Teevens]

I'm trying to finish my physics homework and one of the questions is somewhat philosophical.

Problem:
A cannon ball is shot at noon (12pm), what is faster? The cannon ball or its shadow? That's all the question is :p

 

[Bystander]

The cannon ball or its shadow?

You're firing due north at zero muzzle elevation at the gates of the "walled city of your choice" over a level plain. What's the path of the cannon ball? What's the path of the shadow?

 

[Liam Teevens]

You're firing due north at zero muzzle elevation at the gates of the "walled city of your choice" over a level plain. What's the path of the cannon ball? What's the path of the shadow?

I am not sure as this is my first year of taking physics, but at noon the shadow and the ball would have the same path? They would be the same speed?

 

[Bystander]

You're 1 mile south of the North Pole and firing due east at zero muzzle elevation. Since you're now in an M-1 Abrams your cannon's muzzle velocity is ~ 5,000 feet per second. The time of year is the autumnal, or vernal, equinox, your choice. The Earth's curvature is such that for every mile distant from you a range pole, or levelling rod, or elevation stake will "drop" about 4" below your line of sight. Second shot will be at 1/2 mile south of the pole, again due east, again at the equinox.

 

[Drakkith]

A cannon ball is shot at noon (12pm), what is faster? The cannon ball or its shadow? That's all the question is :p

I don't feel that there's enough information here to answer it. It feels like a trick question.

 

[ehild]

I am not sure as this is my first year of taking physics, but at noon the shadow and the ball would have the same path? They would be the same speed?

The shadow moves on the ground. An the ball?

 

[Borg]

The shadow moves on the ground. An the ball?

Or, a similar question: a ball is thrown straight up at noon - which travels faster, the shadow or the ball?

 

[Bystander]

Or, a similar question: a ball is thrown straight up at noon - which travels faster, the shadow or the ball?

The perfect statement of the question, and the conditions under which it is answered are N or S of 45th parallels (or on) at either equinox.

 

[Borg]

In order to be easier to understand, the question should say something like - A cannon ball is shot while the sun is directly overhead at noon (12pm), what is faster?

The perfect statement of the question, and the conditions under which it is answered are N or S of 45th parallels (or on) at either equinox.

Do you mean the Tropic of Cancer and the Tropic of Capricorn? Those are located at approx. 23°26′ N and S of the equator. Beyond that, the shadow couldn't be directly under an object on any day of the year.
Edit: I see the flaw in my logic now.

 

[Bystander]

Do you mean the Tropic of Cancer and the Tropic of Capricorn?

No. I really do mean 45 degrees N or S parallels --- at noon --- on either equinox.

 

[Borg]

No. I really do mean 45 degrees N or S parallels --- at noon --- on either equinox.

I'm missing something then but I do see a hole in my logic when a ball is thrown straight up at the north pole. In any case, the OP should probably assume that the sun is directly overhead.

 

[Bystander]

Liam, if you could give us a context for the question it would help us a lot coming up with an appropriate answer for you. Chapter headings, one or two of the other questions in the problem set, something to let us "tune in" on just what is being expected of you.
@Liam Teevens

 

[kuruman]

At any instant, the cannon ball travels at a certain speed. Its shadow travels at the speed of the projection (at noon the sunlight is perpendicular to the ground) of the ball's velocity vector on the ground. Therefore, the shadow travels at a speed that is a component of the velocity vector. Which is larger, the magnitude of a vector or its component along some direction?

 

[nasu]

At any instant, the cannon ball travels at a certain speed. Its shadow travels at the speed of the projection (at noon the sunlight is perpendicular to the ground) of the ball's velocity vector on the ground. Therefore, the shadow travels at a speed that is a component of the velocity vector.

Which is larger, the magnitude of a vector or its component along some direction?

This is true twice a year on the equator and once a year for points between the two tropics. It never happens for locations at higher latitudes than 23.5 degrees (N and S).
But the Sun has the maximum height at noon and its rays are the closest to being perpendicular to the ground at this time.
But this maximum height can be quite low during the winter.

I am not saying that your analysis is wrong. Even with rays inclined relative to the vertical, it may apply.

 

[256bits]

I am not sure as this is my first year of taking physics, but at noon the shadow and the ball would have the same path? They would be the same speed?

You might have to re-think "have the same path." One travels through the air, the other along the ground.

Also, the question is somewhat ambiguous, as it leaves out certain conditions, such as latitude, direction, firing angle, muzzle velocity, etc that could have a bearing on the answer.

Problem:
A cannon ball is shot at noon (12pm), what is faster? The cannon ball or its shadow?

You might also want to look at the word "faster", beyond the first impression that that comes to mind. Does that word actualy imply speed or velocity? Perhaps instead it implies time. Or something else? A formulated answer certainly will depend upon the meaning of the word.

As you do say you are just starting out with physics, this type of question seems more to pike your deduction and reasoning powers on problem solving, rather than equation manipulation. What asumptions are important and which ones can be cast aside.

If and when you get enough equations of physics and mathematics under you belt, you may be able to determine something more complex such as determining the parabolic path of the cannon ball through the air and the parabolic path of the shadow traced along the curved ground, and if whether or not the two can ever have the same curvature ( such things as this may interest you, maybe not ) and under what condtions. Your question here is a good one, as you can see by all the interest and responses it has gathered.

Anyways, my answer for the question would be: keeping things simple, of course.
They are both just as fast since they depart and arrive from origin and destination at the same time.