Question

Skiing Differential Equation Please help!

Answer 1

Ohh the Tratrix problem :O this looks familiar. hmm

Answer 2

first order equations, but this doesn't translate well in google translate for me

Answer 3

Were you able to figure out part a?
Looks like we just use the Pythagorean Theorem, yes?

Answer 4

yes, AB= sqrt(400-y^2) is that right, please shoot me down if not

Answer 5

Ok good stuff.

Answer 6

Sooooo this is what I'm thinking for part b.

Answer 7

\[\Large\bf\sf \tan(\pi- \theta)\quad=\quad \frac{y}{AB}\]

Answer 8

yaaas, keep going

Answer 9

Tangent is periodic in pi, therefore,\[\Large\bf\sf \tan(\pi-\theta)\quad=\quad \tan(-\theta)\]And since tangent is an odd function, it has this property,\[\Large\bf\sf \tan(-\theta)\quad=\quad -\tan \theta\]

Answer 10

That allows you to simplify the left side down nicely.

Answer 11

\[\Large\bf\sf \tan \theta\quad=\quad -\frac{y}{AB}\]I think that puts us on the right track there.. hmm

Answer 12

and ab is just sqrt(400-y^2), thank you

Answer 13

cool looks good.
How bout part c? :)

Answer 14

wouldnt it just be the same thing as part b?

Answer 15

i don't know how to explain that

Answer 16

Ya I think it would be the same.

Umm it has something to do with the fact thattttttt...
That diagonal is `tangent to the curve.

So the slope of that diagonal represents the derivative of the curve.
And the slope is given by `rise` / `run`.

Which in this case would be `-y` / `AB`.

negative y since the y is moving down, yes?

Answer 17

yeah you're right , i thought iwas going to write a novel for this problem

Answer 18

looks like we're done here!

Answer 19

yah wasn't too bad!
I thought they were going to make you find the anti-derivative, which is a bit more work :)

Answer 20

thanks for the help :D! it means the world to my education.

Answer 21

one more part to the question
d) Solve the equation for y(x)

Answer 22

https://docs.google.com/document/d/1MCidnRDmwE2RxXkZio0ZbCfYEuAqOZxajf6KW7Yrpyo/edit

click that please

Answer 23

oo a new part :O

Answer 24

yes a new part :(

Answer 25

http://www.twiddla.com/1500497