Question

An object is dropped from the top of a 100m tower. It's height above the ground after tsec is 100-4.9t^2m. How fast is it falling 2 seconds after it dropped?

Answer 1

the m is just the meters notation, not meant to be part of the question as a variable

Answer 2

do you know calculus?

Answer 3

take the derivative and replace \(t\) by 2

Answer 4

i'm attempting to learn it, that's why I'm asking it

Answer 5

so find the derivative, THEN replace t?

Answer 6

oh crap you have to work from the definition
ok not hard

Answer 7

let me try that then get back to you @satellite73

Answer 8

Again, take the derivative (haha....) and substitute 2. The derivative of a position function is speed.

Answer 9

ok it is not hard
or you can use
\[\lim_{t\to 2}\frac{f(t)-f(2)}{t-2}\] if that would be easier

Answer 10

I don't understand how you got that equation..

Answer 11

it is another expression for \(f'(2)\)

Answer 12

Just take the derivative and dont worry about it then... if one way is easier, stick to it.

Answer 13

She hasn't learnt the derivative formulas. Using the definition is VERY hard for this question.

Answer 14

what @baldymcgee6 said. if you have one way, use it.
but you are asked for the derivative at a number, so you can use
\[\frac{f(2+h)-f(2)}{h}\] if you like, since you are working with \(2\) and not \(x\)

Answer 15

It still looks very hard to simply all that with the definition...

Answer 16

in the beginning it is probably easier to work with a number. you put a number in, get a number out

Answer 17

is it 19.6 m/sec?

Answer 18

it is the same as computing
\[\frac{f(t+h)-f(t)}{h}\] and then replacing \(t\) by \(2\)

Answer 19

Yes it is.

Answer 20

I see why you did the equation with replaced 2s, but it seemed to work thank God

Answer 21

and I got it negative, but it's positive because it's speed? and that's always positive?

Answer 22

So much easier with the power rule >.< .

Answer 23

You should say the VELOCITY is positive.

Answer 24

oops.. VELOCITY

Answer 25

yes i think you are right, it is 18.6
in any case it is \(-2\times 4.9\times 2\)

Answer 26

rest assured that in a week you will be able to do this annoying problem instantly in your head

Answer 27

you will say
" the derivative of \(100-4.9t^2\) is \(-9.8t\) and if you replace \(t\) by \(2\) you get \(-9.8\times 2\)"

Answer 28

What satellite73 said. After you learn the derivative formulas it becomes MUCH easier.

Answer 29

IT'LL BE THAT EASY? FML
we're moving to a whole new chapter in the next week...

Answer 30

It will be that easy :P . For instance I can tell you the derivative of e^tan(x) is sec^2 (x)*e^(tan(x) right away :P .