Can a bullet fired reach a percentage of the earths surface?

[JustSomeGuy80]

Homework Statement

I have a problem in which I don't understand what is supposed to be solved. This is the exact question:

"A silo-based Inter-Continental Ballistic Missile has a range of 8000 miles. If the Earth is presumed to be a sphere with circumference 24,000 miles, what percentage of the Earth's surface can be reached by the missile?"

What is meant by the amount of surface that can be reached? Isn't the range of the missile a 1-dimensional number? If so, how can it "reach" a percentage of a 2-dimensional surface area?

Homework Equations

This is an extra credit problem for a 3rd Semester Calculus/Vector Calculus course. That is all the relevant information I can give.

The Attempt at a Solution

I don't recall ever seeing this kind of problem in my current Vector Calculus course. I think it may be a general math question. All I could think of is dividing the range of the missile by the surface area of the earth, but I don't know what kind of dimensional number that would give me, or if its dimensionally correct, or if its even dimensionally possible. Any help would be appreciated.

 

[Mark44]

Homework Statement

I have a problem in which I don't understand what is supposed to be solved. This is the exact question:

"A silo-based Inter-Continental Ballistic Missile has a range of 8000 miles. If the Earth is presumed to be a sphere with circumference 24,000 miles, what percentage of the Earth's surface can be reached by the missile?"

What is meant by the amount of surface that can be reached? Isn't the range of the missile a 1-dimensional number? If so, how can it "reach" a percentage of a 2-dimensional surface area?

Yes, the range is a 1-dimensional number, but you can point the missile in any direction. The means that the missile can reach any point in a circle on the Earth's surface. This circle would be a two-dimensional region.

Homework Equations

This is an extra credit problem for a 3rd Semester Calculus/Vector Calculus course. That is all the relevant information I can give.

The Attempt at a Solution

I don't recall ever seeing this kind of problem in my current Vector Calculus course. I think it may be a general math question. All I could think of is dividing the range of the missile by the surface area of the earth, but I don't know what kind of dimensional number that would give me, or if its dimensionally correct, or if its even dimensionally possible. Any help would be appreciated.

 

[wumple]

My understanding of the problem is that the missile can be fired 8,000 miles in any direction, creating an area around it which it could potentially reach. Then divide the total area that is in range of the missile by the total area of the Earth.

 

[JustSomeGuy80]

Got it. Thanks Wumple and Mark.