Falling Ball:
When an object is allowed to fall freely near the surface of the earth, the gravitational pull is such that the object falls 16 ft in the first second, 48 ft in the next second, 80ft in the next second, and so on.
a) Find the total distance a ball falls in 6seconds
b) Find a formula for the total distance the ball falls in n seconds

- Babynini

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- schrodinger

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- Babynini

@jtvatsim Whenever you're free! I'll try to work it out on my own until then :)

- jtvatsim

Sounds good, be back. :)

- Babynini

a_6=496feet

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## More answers

- Babynini

^ (part a)

- Babynini

b) the formula would be
a_n=16+(n-1)(32)

- Babynini

Testing it with a_2 the formula seems to be correct :)

- anonymous

I got the same thing for b, but 576 for a

- Babynini

hmm let's see where I might've messed up
a_6=16 +(6-1)(32) correct yeah?

- anonymous

to find the 6th term, yes. But I think it's asking for the sum of the first 6 terms

- Babynini

oooh, wow. I completely missed that.

- Babynini

so i must find a_4 and a_5

- Babynini

a_4=112, a_5 = 144

- anonymous

for this one it's easy enough to do that, but there's a formula to find the sum of the first n terms.\[S _{n}=\frac{ n }{ 2 }(a _{1}+a _{n})\]

- Babynini

oh o.0

- anonymous

Yes those are right

- Babynini

hm but I should probably use that formula you just used because the prof introduced it to us.

- Babynini

a_6=176 correct?

- anonymous

yes

- Babynini

so we have
s_6=(6/3)(16+176)
=3(192)
=576

- anonymous

yep

- Babynini

Fantastic! thank you so much :)

- anonymous

you're welcome!

- Babynini

oh wait! @peachpi the b) asks "TOTAL distance the ball falls at n seconds"

- Babynini

my formula is not for the sum

- Babynini

Right?
So the formula would actually be
s_n=(n/2)(16+a_n)

- anonymous

right, and you'd so substitute the formula for the nth term for a_n

- anonymous

If you need an explicit formula

- Babynini

ok, it just asks for a formula that could generate any nth term.

- Babynini

Er, should I put the formula to find
a_n
and also the formula for finding the sums?

- anonymous

so I think what they're asking is for a formula where you would just stick in the n value and get the sum.
Sn = 3(16 + a_n)
but since we know a_n = 16+(n-1)(32)
Sn = 3(16 + 16+(n-1)(32))

- anonymous

does that make sense? can't really think of a right way to say it

- Babynini

you mean
sn=n/6(16+(n-1)(32))
(not ^3)

- Babynini

ahh yes I see what you did.

- anonymous

oh, yes. n/2

- Babynini

ok :)

- Babynini

thanks, phew. That was close. I almost put the wrong formula xP

- Babynini

Sn = (n/2)(16 + 16+(n-1)(32))
is the final formula?

- anonymous

yes. I mean you can do some algebra to make it prettier, but it's correct

- Babynini

oh o.0 we should probably make it prettier.. hah

- Babynini

sn=(n/2)(16+512(n-1))
is that still correct? and simplified enough?

- anonymous

keep going until you get a quadratic, so distribute 512 and combine like terms

- anonymous

wait no!

- anonymous

|dw:1433989465521:dw|

- Babynini

aiai too simplified we never did that in class hrm

- Babynini

maybe up to the second thing you did

- Babynini

(n/2)(32+(n-1)(32))

- Babynini

does that work?

- anonymous

yes

- Babynini

ah ok. I think thats simplified enough o.0

- anonymous

cool

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