Babynini
  • Babynini
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Babynini
  • Babynini
@jtvatsim Whenever you're free! I'll try to work it out on my own until then :)
jtvatsim
  • jtvatsim
Sounds good, be back. :)
Babynini
  • Babynini
a_6=496feet

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Babynini
  • Babynini
^ (part a)
Babynini
  • Babynini
b) the formula would be a_n=16+(n-1)(32)
Babynini
  • Babynini
Testing it with a_2 the formula seems to be correct :)
anonymous
  • anonymous
I got the same thing for b, but 576 for a
Babynini
  • Babynini
hmm let's see where I might've messed up a_6=16 +(6-1)(32) correct yeah?
anonymous
  • anonymous
to find the 6th term, yes. But I think it's asking for the sum of the first 6 terms
Babynini
  • Babynini
oooh, wow. I completely missed that.
Babynini
  • Babynini
so i must find a_4 and a_5
Babynini
  • Babynini
a_4=112, a_5 = 144
anonymous
  • 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
  • Babynini
oh o.0
anonymous
  • anonymous
Yes those are right
Babynini
  • Babynini
hm but I should probably use that formula you just used because the prof introduced it to us.
Babynini
  • Babynini
a_6=176 correct?
anonymous
  • anonymous
yes
Babynini
  • Babynini
so we have s_6=(6/3)(16+176) =3(192) =576
anonymous
  • anonymous
yep
Babynini
  • Babynini
Fantastic! thank you so much :)
anonymous
  • anonymous
you're welcome!
Babynini
  • Babynini
oh wait! @peachpi the b) asks "TOTAL distance the ball falls at n seconds"
Babynini
  • Babynini
my formula is not for the sum
Babynini
  • Babynini
Right? So the formula would actually be s_n=(n/2)(16+a_n)
anonymous
  • anonymous
right, and you'd so substitute the formula for the nth term for a_n
anonymous
  • anonymous
If you need an explicit formula
Babynini
  • Babynini
ok, it just asks for a formula that could generate any nth term.
Babynini
  • Babynini
Er, should I put the formula to find a_n and also the formula for finding the sums?
anonymous
  • 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
  • anonymous
does that make sense? can't really think of a right way to say it
Babynini
  • Babynini
you mean sn=n/6(16+(n-1)(32)) (not ^3)
Babynini
  • Babynini
ahh yes I see what you did.
anonymous
  • anonymous
oh, yes. n/2
Babynini
  • Babynini
ok :)
Babynini
  • Babynini
thanks, phew. That was close. I almost put the wrong formula xP
Babynini
  • Babynini
Sn = (n/2)(16 + 16+(n-1)(32)) is the final formula?
anonymous
  • anonymous
yes. I mean you can do some algebra to make it prettier, but it's correct
Babynini
  • Babynini
oh o.0 we should probably make it prettier.. hah
Babynini
  • Babynini
sn=(n/2)(16+512(n-1)) is that still correct? and simplified enough?
anonymous
  • anonymous
keep going until you get a quadratic, so distribute 512 and combine like terms
anonymous
  • anonymous
wait no!
anonymous
  • anonymous
|dw:1433989465521:dw|
Babynini
  • Babynini
aiai too simplified we never did that in class hrm
Babynini
  • Babynini
maybe up to the second thing you did
Babynini
  • Babynini
(n/2)(32+(n-1)(32))
Babynini
  • Babynini
does that work?
anonymous
  • anonymous
yes
Babynini
  • Babynini
ah ok. I think thats simplified enough o.0
anonymous
  • anonymous
cool

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