PEG Judge - Hard Question

Hard Question

A stone is dropped into a well. t seconds later, a splash is heard. The acceleration due to gravity is g metres per second per second, and the speed of sound is c metres per second. Calculate the depth of the well and the downwards velocity with which the stone hits the water.

Input Format

Line 1: The value of g (0 < g ≤ 1000)

Line 2: The value of c (0 < c ≤ 1000)

Line 3: The value of t (0 < t ≤ 1000)

Output Format

Line 1: The depth of the well in metres.

Line 2: The speed of the stone as it hits the water, in metres per second.

Sample Input

9.80
334
3.41

Sample Output

51.90
31.90

Your answers must have a relative or absolute error of less than 0.01.

Notes

The following equations may be useful:

$\Delta \vec{d} = \vec{v} \Delta t$
$\vec{v}_2 - \vec{v}_1 = \vec{a} \Delta t$
$\Delta \vec{d} = \frac{1}{2} (\vec{v}_1 + \vec{v}_2) \Delta t$
$\Delta \vec{d} = \vec{v}_1 \Delta t + \frac{1}{2} \vec{a}(\Delta t)^2$
$\Delta \vec{d} = \vec{v}_2 \Delta t - \frac{1}{2} \vec{a}(\Delta t)^2$
$\|\vec{v}_2\|^2 - \|\vec{v}_1\|^2 = 2\vec{a}\cdot \Delta \vec{d}$

Here $\Delta t, \Delta \vec{d}, \vec{v}, \vec{v}_1, \vec{v}_2, \vec{a}$ represent time, displacement, velocity, initial velocity, final velocity, and acceleration, respectively.

All Submissions
Best Solutions

Point Value: 3
Time Limit: 2.00s
Memory Limit: 16M
Added: Jan 16, 2009
Author: bbi5291

Problem Types: [Show]

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

Comments (Search)

eric574 on Sep 01, 2018 - 4:12:29 pm UTC Judge is wrong

(0/0)

Looks like the judge was wrong...

Looks like the judge was wrong...

magicalsoup on Sep 01, 2018 - 8:01:03 pm UTC Re: Judge is wrong

(0/0)

yeah, its because of the rounding error, jargon manually most of the submissions, but its still not fixed yet

yeah, its because of the rounding error, jargon manually most of the submissions, but its still not fixed yet

jargon on Sep 03, 2018 - 1:03:13 am UTC Re: Judge is wrong

(0/0)

Actually, it has been fixed, so manual rejudging shouldn't be necessary now.

Actually, it has been fixed, so manual rejudging shouldn't be necessary now.

magicalsoup on Feb 16, 2018 - 11:48:44 pm UTC jargon senpai! please help me

(1/0)

my physics seems right, but why am i getting WA? can you please tell me if its a formating error/round error of algorithm error, help me please, thank you!

my physics seems right, but why am i getting WA? can you please tell me if its a formating error/round error of algorithm error, help me please, thank you!

magicalsoup on Feb 16, 2018 - 11:49:06 pm UTC Re: jargon senpai! please help me

(1/0)

rounding or algorithm error

rounding or algorithm error

jargon on Feb 17, 2018 - 7:11:38 am UTC Submissions rejudged.

(1/0)

1. Please make use of the edit function instead of posting multiple comments in a row. You can edit your comments by clicking the pencil icon on the left side of your comment.

2. Our [i]sincerest[/i] apologies. This problem was effectively impossible for a while, due to an error on our end. I have resolved this error, and [b]I manually rejudged several affected submissions[/b] (at least one from each user who posted since the mistake); the number of accepted users has increased from 49 to 63.

Please resubmit if I missed you or you believe you may have been affected.

1. Please make use of the edit function instead of posting multiple comments in a row. You can edit your comments by clicking the pencil icon on the left side of your comment.

2. Our sincerest apologies. This problem was effectively impossible for a while, due to an error on our end. I have resolved this error, and I manually rejudged several affected submissions (at least one from each user who posted since the mistake); the number of accepted users has increased from 49 to 63.

Please resubmit if I missed you or you believe you may have been affected.

asdflkjh on Mar 28, 2017 - 12:47:49 am UTC What does per second per second mean?

(0/0)

What does per second per second mean?
[quote]The acceleration due to gravity is g metres per second per second[/quote]

What does per second per second mean?

The acceleration due to gravity is g metres per second per second

jargon on Mar 28, 2017 - 8:58:52 am UTC Re: What does per second per second mean?

(0/0)

This will make sense once you've had exposure to elementary physics.

This will make sense once you've had exposure to elementary physics.

asdflkjh on Apr 10, 2017 - 9:41:29 pm UTC Re: What does per second per second mean?

(0/1)

per second per second?
it repeats twice!

per second per second?
it repeats twice!

jargon on Apr 12, 2017 - 12:19:04 am UTC Re: What does per second per second mean?

(0/0)

the short of it:

how fast you go is change in displacement, measured in [metres] per second. (velocity.)
how fast you're increasing how fast you go is change in velocity, measured in [metres per second] per second. (acceleration.)

the short of it:

how fast you go is change in displacement, measured in [metres] per second. (velocity.)
how fast you're increasing how fast you go is change in velocity, measured in [metres per second] per second. (acceleration.)

IMAGenius on Dec 31, 2016 - 8:22:53 pm UTC

(1/1)

I'm not sure why my program doesn't work

I'm not sure why my program doesn't work

jargon on Jan 02, 2017 - 7:44:02 am UTC Re: ...

(1/1)

You are experiencing significant loss of precision.

Edit: I was wrong. Your code was right, and the judge was wrong. I apologise.

You are experiencing significant loss of precision.

Edit: I was wrong. Your code was right, and the judge was wrong. I apologise.

Butane on Jan 12, 2014 - 12:05:56 am UTC Rounding for this question?

(0/0)

OK, so I tried all sorts of rounding methods, but I keep getting the wrong answer. In the sample input, my program rounds the speed of the stone to 31.93. How was the sample input rounded, because the full answer is around 31.929799, yet the sample output says only 31.90?

OK, so I tried all sorts of rounding methods, but I keep getting the wrong answer. In the sample input, my program rounds the speed of the stone to 31.93. How was the sample input rounded, because the full answer is around 31.929799, yet the sample output says only 31.90?

ImbaCalvin on Jan 12, 2014 - 1:38:21 am UTC Re: Rounding for this question?

(1/1)

The exact answer is actually
51.9029278687
31.8950997212

The exact answer is actually
51.9029278687
31.8950997212

ilovepi on Jan 15, 2011 - 10:20:28 pm UTC HOW?

(0/1)

How are you supposed to do this questions? How come it's so hard when it's only worth 3 points? If anybody knows, can they give me the formuala in words that I can actually UNDERSTAND? THANK YOU!!!

How are you supposed to do this questions? How come it's so hard when it's only worth 3 points? If anybody knows, can they give me the formuala in words that I can actually UNDERSTAND? THANK YOU!!!

bbi5291 on Jan 15, 2011 - 10:31:08 pm UTC Re: HOW?

(0/0)

It's not hard; it just requires a basic understanding of high school algebra and physics. The point value stands. (I even gave you the equations of kinematics you need to solve this!)

It's not hard; it just requires a basic understanding of high school algebra and physics. The point value stands. (I even gave you the equations of kinematics you need to solve this!)

ilovepi on Jan 16, 2011 - 6:00:24 pm UTC Re: Re: HOW?

(0/0)

Well then could you tell me the meaning of the equations? It's so hard to understand when your only in grade 7.

Well then could you tell me the meaning of the equations? It's so hard to understand when your only in grade 7.

bbi5291 on Jan 17, 2011 - 12:36:47 am UTC Re: Re: HOW?

(0/0)

These equations describe uniformly accelerated linear motion, where Δ[i]t[/i] is elapsed time, Δ[b]d[/b] is displacement, [b]v[/b]₁ is initial velocity, [b]v[/b]₂ is final velocity, and [b]a[/b] is acceleration.

These equations describe uniformly accelerated linear motion, where Δt is elapsed time, Δd is displacement, v₁ is initial velocity, v₂ is final velocity, and a is acceleration.

SourSpinach on Jan 17, 2011 - 4:04:04 am UTC Re: Re: HOW?

(0/0)

I recommend simply not doing this question until you've taken Grade 11 Physics.

I recommend simply not doing this question until you've taken Grade 11 Physics.

ilovepi on Jan 18, 2011 - 12:18:22 am UTC Re: Re: HOW?

(0/0)

I will listen to your advice. TY.

I will listen to your advice. TY.

HelloMelloC on Jan 27, 2011 - 3:36:59 pm UTC Re: Re: HOW?

(0/0)

LOL.
No need for physics here, I just BF'ed.
Digital technology's so great (compared to analog) as you can just set an arbitrary precision depending on how precise the situation needs (with the equivalent time costs, of course).

LOL.
No need for physics here, I just BF'ed.
Digital technology's so great (compared to analog) as you can just set an arbitrary precision depending on how precise the situation needs (with the equivalent time costs, of course).

frenzybenzy on Jan 18, 2009 - 2:01:39 am UTC Anything wrong?

(0/0)

I can't find anything wrong in my equation.

I can't find anything wrong in my equation.

DrSane on Jan 18, 2009 - 2:09:42 am UTC Re: Anything wrong?

(0/0)

I haven't read the problem, so I can't comment on who's doing what right, but Sour Spinach has a different algorithm  to get 5/5. Notice the time his solution took.

[b]Edit[/b]: But, according to the analysis, it's not necessary. So I don't actually know what's going on.

I haven't read the problem, so I can't comment on who's doing what right, but Sour Spinach has a different algorithm to get 5/5. Notice the time his solution took.

Edit: But, according to the analysis, it's not necessary. So I don't actually know what's going on.

bbi5291 on Jan 18, 2009 - 3:02:23 am UTC Re: Anything wrong?

(2/0)

Aah, you don't know how close you are! You forgot to divide by 2 when using the fourth equation, most likely.

Aah, you don't know how close you are! You forgot to divide by 2 when using the fourth equation, most likely.

frenzybenzy on Jan 18, 2009 - 3:05:32 am UTC Re: Re: Anything wrong?

(0/0)

THANK YOU SO MUCH

THANK YOU SO MUCH

Bob on Jan 17, 2009 - 1:26:36 am UTC Why is this only two points?

(1/0)

How do people in Grade 6-7 do this program (how is it only 2 points!!!)? We don't know anything about this physics stuff (or something like that).

How do people in Grade 6-7 do this program (how is it only 2 points!!!)? We don't know anything about this physics stuff (or something like that).

bbi5291 on Jan 17, 2009 - 2:52:45 am UTC Re: Why is this only two points?

(1/0)

It's for didactic purposes only. Although, since, when I think of it, the same can be said for all problems on the judge, I guess it should be 3 points, since it's harder than A plus B, and around the difficulty of an easy CCC problem.

It's for didactic purposes only. Although, since, when I think of it, the same can be said for all problems on the judge, I guess it should be 3 points, since it's harder than A plus B, and around the difficulty of an easy CCC problem.

Bob on Jan 17, 2009 - 3:02:30 am UTC Re: Re: Why is this only two points?

(0/0)

Thanks for the equations! :smile:

Thanks for the equations!