Calculating Highway Truck Length for Nuclear Bomb Yield

[kraigandrews]

Homework Statement

The energy released by nuclear bombs is measured in kiloton (kt) or megaton (Mt) units. One kiloton is a unit of energy released by 1000 tons of trinitrotoluene (TNT). One kiloton is 4.2×1012 joules. The yield of fission bombs is typically between 10 and 500 kilotons, the yield of fusion bombs is between 1 and 50 megatons. Calculate the length of a single line of large highway trucks carrying a 74.0 kt load. The capacitity of one truck is 28.0 t, the length of one truck is 15.0 m. The spacing between the trucks is 21.0 m.

The Attempt at a Solution

So i divided 74000 tons by 28 tons to get 2642.857 trucks then multiplied by the length of one truck to get 39642.857 then added (21*(2642.857-2)) to get the spacing included, i subracted two because there is no spacing before the first truck and none after the last truck. but this is incorrect what did i do wrong

 

[Delphi51]

How are you thinking of the spacing? Before each truck or after it? Not both.

 

[kraigandrews]

well there would be spacing between every truck except the first and last truck

 

[cjl]

How would there be 0.857 of a truck? I would guess they want you to round up, since you can't have a partial truck.

 

[kraigandrews]

True I was just keeping it into be more exact because the question is asking for how many trucks but how long the convoy is.

 

[PeterO]

Homework Statement

The energy released by nuclear bombs is measured in kiloton (kt) or megaton (Mt) units. One kiloton is a unit of energy released by 1000 tons of trinitrotoluene (TNT). One kiloton is 4.2×1012 joules. The yield of fission bombs is typically between 10 and 500 kilotons, the yield of fusion bombs is between 1 and 50 megatons. Calculate the length of a single line of large highway trucks carrying a 74.0 kt load. The capacitity of one truck is 28.0 t, the length of one truck is 15.0 m. The spacing between the trucks is 21.0 m.

The Attempt at a Solution

So i divided 74000 tons by 28 tons to get 2642.857 trucks then multiplied by the length of one truck to get 39642.857 then added (21*(2642.857-2)) to get the spacing included, i subracted two because there is no spacing before the first truck and none after the last truck. but this is incorrect what did i do wrong

Your length of trucks is correct - though should be rounded up to2643 trucks.

kiven you are expressing to 3 figure precision only 39.6 km of truck covers the round off anyway.
since the "spacing" is even longer than a truck - the line of trucks will be over 90 km long.
What was the answer you were given?

 

[kraigandrews]

Nevermind I got it but thanks for the help.