Question

To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. When an object is dropped from a tall building, it falls about 16 feet in the first second, 48 feet in the second second, and 80 feet in the third second, regardless of its weight. How many feet would an object fall in the tenth second?

Answer 1

Physics problem logic: Air resistance is somehow excluded.

Answer 2

*It's using Arithmetic Sequence remember*

Answer 3

Huh?

Answer 4

It's not dealing with physics, it's a word problem based on Arithmetic Sequence

Answer 5

I am talking about fact that Galileo tried to prove that different objects falls at same rate. It won't go well since there is air resistance. Just tease on it....

Anyway, so to apply arithmetic sequence here, we have first term as 16, second term, and 80 as third term.

\(48-16 = 32\) and \(80-48=32\)

So we can see that common difference is 32.

So you have \(a_t = -16+32t\), where t is second.

Answer 6

48 as second term*

Answer 7

Openstudy is lagging so bad here :/

Answer 8

I am sorry and yes 48 is the second term

Answer 9

Can you find \(a_{10}\)?

Answer 10

Now I reread the problem, it just say "object with different weight"

So my bad... But problem still makes no sense. Objects don't fall down at constant speed LOL

Answer 11

what's

a of n
a of 1
n
d

Answer 12

@geerky42

what's

a of n
a of 1
n
d

Answer 13

You mean \(a_n = a_1+(n-1)d\)?

Well, what I used is \(a_n = a_0+nd\)

It's the same thing since \(a_0 = a_1-d\)

We already figured \(d\), which is \(32\).

Since first term is \(a_1=16\), we can figure out \(a_0\); \[a_0 = a_1-d = 16-32 = -16\]

So now we have \(a_n = -16+32n\)

From here, you can figure \(a_{10}\) by plug in \(n=10\)