A cannon ball leaves a fort with an initial horizontal speed of 1.8*10^2 m/s and strikes a ship in the sea below 7.2 s later. How high is the fort above sea level?

## How high is the fort?

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# 3 Answers

Initial height : Δy=½gt² =½(9.8)(7.2)² = 250 m.

Note that the answer is independent of the initial horizontal velocity.

Hey Sun -- constant g ... use your delta V's of 10 @ sec ... Vdn at sea is 72m/s ...

Vave is 36m/s ... freefall 36m/s for 7.2s ==> 210 +42 +7 ~260m ... Regards :)

This takes a little longer to explain, instead of looking up a strange formula on a

formula sheet or even worst trying to memorize the formulas - but I think it is easier.

You can find the answer using the same smarts you use to figure out how much money

you need to buy 10 candy bars a day for the next 7 days if candy bars are $10.00 (or $9.81).

You can use the formulas or think of it this way.

1 - One important thing to remember with falling object or X & Y problems

is that the

**X and Y are independent**. Always. So for this we Only need to solve a Y or falling problem.

2- What is the starting velocity? Zero - 0

3- After 7.2 seconds falling (when it hit the water) how fast was it going?

7.2 sec. X 10 meter per sec. increase every sec. = 7.2 s X 10 m/s

^{2}= 72 m/s (if you want to make the problem harder and be a minuscule

2.5% more accurate you can use 9.81 m/s

^{2}instead of 10 m/s^{2})4- Okay now you know the starting speed and the ending speed;

what was the average speed? (0 + 72) ÷ 2 = 36 so an average of 36 m/s

5- Good! Now, if something goes an average of 36 m/s for 7.2 s, how far does it go?

36 m/s for 7.2 s = 36 m/s X 7.2 s = 260 m

6) So it fell 260 m therefor the fort was 260 m above sea level.

(Using 9.81 instead of 10 would give 254 - we were 2.4 % high)

## Comments

constantacceleration. If you do not specify this, students may blindly apply the same trick to the variable acceleration.Kirill, You are absolutely right about the 0 starting velocity. In this problem we are solving only the vertical so I just considered only that. For a student that needs my explanation to 'get it' they would automatically see what I did, I need to remember to point that out, thanks.

You talk about physics in 7th grade (they do have physical science sometimes). You are definitely right. We do not teach science properly here in the US. Imagine if in in 9th grade everyone learned all Spanish and took a test at the end of the year. Then in 10th all French and had a test; German in 11th, and Latin in 12th! Everyone knows you can't learn a language in a year; but expects kids to learn a whole branch of science.

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