# Physics: Problem of the Week 09/02/2004!

#### masterazn

##### Banned
Physics: Problem of the Week 09/02/2004!

A car rolls down a hill into a very large haystack. Suppose the height of the hill is doubled, approximately how much further would the same car go into the same haystack?

a) twice
b) thrice
c) four times
d) none of the above

Why?

#### Wuhan_Clan

##### Diabloii.Net Member
Twice as much. If the hill was twice as high, twice as much potential gravitational energy is stored and twice as much energy is required to stop it.

This assumes that the haystack applies a constant resistive force and not like a spring.  (this won't matter so nvm)

man, late night math seems so much harder - i wonder if i should sleep now or just stay awake all night and sleep after my moring classes

#### masterazn

##### Banned
I say go to sleep. Thanks.

#### asdf

##### Diabloii.Net Member
yeah, it really depends on the physics of the haystack.

#### masterazn

##### Banned
Well......it's just a haystack.

#### asdf

##### Diabloii.Net Member
which is a big problem because i don't know exactly how haystacks react to impact.

cushions i guess

#### Wolfwind

##### Diabloii.Net Member
Goddamnit stop helping kids with their homework..

Just kidding. And if I remember rightly it's force by distance, so yeah. I'd say double. But then again I took Biology at A Level ^_^

#### Crimh

##### Diabloii.Net Member
Somewhere in the back of my head, I have this itch telling me that it is four times..But no, I can't remember why :idea:

#### Avalon

##### Diabloii.Net Member
Potential Energy: MassxGravityxHeight
Kinetic Energy: 1/2MassxVelocity^2

PE determines maximum KE for a given move. Doubling the height, all other factors equal, would double the PE.

ForcexDistance= Work, in which case. The car itself isn't really doing any, as it's just relying on gravity.

Eh. Someone pick up from there.

#### masterazn

##### Banned
Eh? right triangle? four times? HELP!!!!!

#### Jigga-Scrooge

##### Diabloii.Net Member
it depends on how big the hill is. you know, the car can only go so fast. so if the first hill was big enough to get it up to max speed, then the second would be at max speed too so it would be the same.

#### masterazn

##### Banned
Dammit, there has to be something to this.

#### ragnar_ii

##### Diabloii.Net Member
4 times. that is assuming there is no friction(which is the case in most basic physics classes) this answer is derived using the kinematic equation
v(final)^2 = v(initial)^2 + 2*a*d. where v is velocity, a is accelortion and d is displacement. with this equation you will see that doubling the displacment will quadruple the speed thus quadrupling the force bringing the car four times further through the haystack.

#### asdf

##### Diabloii.Net Member
um... no. speed is increased by sqrt(2). check your calculations again.

and anyway, if they haystack provides a constant force, the distance increases by sqrt 2. if it's like a spring then it's still sqrt2 for different reasons. if it's similar to air resistance or something different it's a lot harder. the question doesn't specify the equations of the haystack do they?

##### Banned
This is easy, you just have to state your assumptions first to get away with it.

First, state the the first hill was so high that the car reached terminal velocity before it hit the haystack. (this means its going as fast as natural gravity will allow it)

Thus, no matter how high the second hill is, the car will be travelling at the same speed as before upon entering the haystack. So, it will go the same distnance into the stack.

Its nice that everyone else is tossing all these formulas around, but just keep it simple and state your assumptions. Since they dont give you an initial hill height, you can assume it to be anything, and be right.

#### Underseer

##### Diabloii.Net Member
ASDF is right.

V2 = sqrt(2) * V1

So I'm not at all confident the result will come out to an integral multiple.

#### Geeno

##### Diabloii.Net Member
Screw calculus based physics I say, basic algebra is the world I live in! Anything not done in algebra is infact witchcraft!

#### Smelly

##### Diabloii.Net Member
The person who made this question should be fired from his job. I don't know too much about mathematical problems, but this is the way I see it...

You get a 40 foot hill, that has a distance of, I dunno, 90 feet. You double the height of the hill, thus increasing the length of the hill (since it will be at an angle?) and then you get 80 ft and 180 ft. Regardless of how fast you go, you will still travel 180 ft, correct?

This question seems too vague as it's not really asking for specifics, and to be honest I don't believe the haystack has anything to do with the problem at all. I say make up a solution for distance, speed, and time each, and then ask the professor what kind of drugs he was using when he made such a crappy question?

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