The ill-prepared adventurer
Ragknot
posted by Ragknot at
12:00 AM
Sunday, December 28, 2008
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12 Comments:
Hmm... tough to solve actually but I have an answer but im not sure of it.
Now none of my answers are exactly right because u have to use sin and cos and i used the decimal values.
now the 2 most direct routes to the river are going vertical and horizontal.
With this it is really easy there are 2 ways for him to go:
a)if x=7 .................y=17.11
b)t if x=20, ............y=30.31
and both these routes take only:
a)x is same y changes from 30-17, i.e. distance travelled is around 13 miles.
b)y is same x is changes from 7-20, i.e. around 13 miles again.
So these both instances should be no problem for him to travel.
Since the adventurer can travel 15 miles max in any direction, the furthest place he can reach is determined by the function
(x-7)²+(y-30)²=r²
where r ≤ 15.
since we know that the river follows
y=10sin(x/10)+10cos(x/5)+x
we can substitute y in and solve for r
(x-7)²+(y-30)²=r²
(x-7)²+(10sin(x/10)+10cos(x/5)+x-30)²=r²
if we graph
r=sqrt(x-7)²+(10sin(x/10)+10cos(x/5)+x-30)²)
the absolute minimum is where r is the smallest, meaning the shortest distance to the river.
The shortest distance is 14.7623 miles when x=6.1096
"guessing" how many miles you can go is not at all accurate.
take into consideration that they DO have 15 miles left before they dehydrate; 15 miles assumes that they are going at a constant speed, but what if they slow thier speed down, would that mean dehydration would come earlier, or remaining the same (which does not make sense at all unless they had more time to begin with allowing for longer travel)
also, suggest they go faster than the constant rate, will they still dehydrate after the 15 miles? or will they die in the same alloted TIME?
also, the traveller assuming the 15 miles did not take in account an increase in temperature causing the dehydration to take in effect sooner.
he was stupid in the first place by not travelling near the river
Sam ,
U r using pythagoras theorem to find a diagonal route. I thought about that too but that distance comes more than the distance needed to go vertical or horizontal directly that is why i did not write about it. Because going diagonal it will take him more distance. I got answer as around 13 miles. But as you have said diagonal comes to around 15 miles and as the question was the nearest route i gave my answer.
Ragknot....could u tell us if we are right or wrong??
To all
Yes I can tell you if you're right or not.
AJK - on your first post, I can't see where ~13 came from. I don't think it could be right.
Sam - amazing
Anonymous -yesh, you're right, he wasn't smart. But if he goes due south or due east, he might make it.
AJK - I don't know that he used Pythagoras therorm. I didn't and got Sam's same results.
To AJK
The equation I used was not Pythagoras Theorem per se. It is the general equation for a circle.
(x-p)²+(y-q)²=r²
where (p, q) is the centre of the circle and r is the radius.
Also I did this in radians while you did this in degrees so our answers will be different.
To find the shortest distance, use the distance formula to get squareroot((7-(10sin(x/10)+10cos(x/5)+x))^2+(30-x)^2). Then, take the derivative and set that equal to zero to find the x value that gives the shortest distance from (7,30), which is approximately 6.1096327639267. Plugging that in yields a y value of about 15.264559033908, so the closest point to the adventurer is (6.1096327639267,15.264559033908), and his distance from the river is approximately 16.441848284476.
To find the shortest distance, use the distance formula to get squareroot((7-(10sin(x/10)+10cos(x/5)+x))^2+(30-x)^2). Then, take the derivative and set that equal to zero to find the x value that gives the shortest distance from (7,30), which is approximately 6.1096327639267. Plugging that in yields a y value of about 15.264559033908, so the closest point to the adventurer is (6.1096327639267,15.264559033908), and his distance from the river is approximately 14.7623160202.
Sorry for the distance I got earlier. Must have plugged in the wrong numbers.
i did the exact same thing as the above guy did and so concluded that he cannot reach the river but apparently he can
its fundamentally same as Sam's method but answer is different
Don't know where i went wrong
if anyone can explain it would be appreciated
checked the calculations again
i guess the idiot adventurer just about makes it to the river
Hehehe....Nerds!!!
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