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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

@jtvatsim Whenever you're free! I'll try to work it out on my own until then :)
Sounds good, be back. :)
a_6=496feet

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

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

Not the answer you are looking for?

Search for more explanations.

Ask your own question