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A catapult can launch a plane from the deck of an aircraft carrier from 0 to $260 \mathrm{km} / \mathrm{h}$ in $2.0 \mathrm{s}$. How many $\mathrm{g}$ 's is the average acceleration for such a launch? $\left(1 \mathrm{g}=9.8 \mathrm{m} / \mathrm{s}^{2}$.) \right.

$3.7 \mathrm{g}^{\prime}$

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 1

Applications of the Indefinite Integral

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So the average acceleration, I'm glad to note average a it's equal to our change in velocity divided by our change in time. So here are change in velocity was equal to 260 and this was in km our minus zero kilometers per hour since we were told it went from 0 to 260 kilometers per hour in two seconds. And so what we want to do here is we want to actually convert this kilometers per hour into um meters per second. So Since this is equal to 260 km/h, we're going to multiply by 1000 m per one kilometer and then by one our for 60 minutes And then by one minute For 60 seconds so that we can get this value into meters per second. So 260 times 1000 is 260,000. So this would be equal to 260,000 Divided by 3600. And this was this is in now meters per second. So if you plug this into calculator 260,000, Divided by 3600, it's equal to 72 .22 feeding and this is in m per second. And so now that we have this average um velocity in meters per second, we can go back and look at our average acceleration equation. She is equal to our average velocity divided by our average or sorry, or change in velocity divided by our change in time. And so now we can put our change in velocity is 72.22 m/s and we can divide by two seconds since we're going from were just we were only accelerating in those two seconds. So we have our average Acceleration is equal to 72 .22 repeating meters per second, divided by two seconds. And so this is equal to 36 .11 repeating meters per second squared. And so this is our average acceleration. Now to figure out how many jesus is we just multiply this. So RGs, it's going to be equal to three, sorry, 36.11 m per second squared times one, divided by It was 9.8 meters per second square. Okay, so now our units are going to cancel and we're just going to have Um, RGs is equal to 36.11 Repeating, divided by 9.8. And so if you plug this into a calculator, this comes out to be 3.68 five Gs. So our average acceleration was again 70 or sorry, 36.11 m per second squared. And then to convert that into Gs, we have 3.685 Gs.

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