Question

parametric equations help

Answer 1

@electrokid here u got ur new challenge

Answer 2

arc length:
\[
dL=\sqrt{x'(t)^2+y'(t)^2}
\]

Answer 3

times dt

Answer 4

hmmm...please go ahead

Answer 5

so,
\[
s=\int_{u=0}^\pi\sqrt{\left(\frac{df}{du}\right)^2+\left(\frac{dh}{du}\right)^2}\;du
\]

Answer 6

its o to pi...right?

Answer 7

yes

Answer 8

got it...how will we calculate about skier

Answer 9

he'd travel half that distance

Answer 10

ok i know how to integrate x and y but this stuff kills me, i totally get confused while integrating df/du and those type of equations

Answer 11

you cannot integrate this since you do not have the functions f(u) and h(u)
they just wan you to write the expression for evaluating it

Answer 12

oh...i was worthlessly freaking out...thanks...would you go ahead for c?

Answer 13

for the rest, they gave us the Work-Energy Thm
\[
{1\over2}mv^2+mgy=k
\]
m = mass of the skier
v = velocity/speed of the skier
g = 1.81m/s^2 = acc due to gravity
y = height from where the person skies
k = amount of work done = const.

Answer 14

(c) set v=0
we get \[mgy=k\] but it is give in the very first line of the problem that the skier starts at y=1
so, \[mg=k\]
QED

Answer 15

awesome...wish i would be good at word problems...whats v in terms o s

Answer 16

in my above post, I showed you the differential arc length. use that

Answer 17

velocity of skier?

Answer 18

hmm
\[v={ds\over dt}=S/T\]

Answer 19

\[
{1\over2}m\left(ds\over dt\right)^2=k-mgy\\
{1\over2}m\left(ds\over dt\right)^2=mg-mgy\\
\left(ds\over dt\right)^2={mg(1-y)\over{1\over2}m}\\
\left(ds\over dt\right)=\sqrt{g(1-y)}
\]

Answer 20

f, g, h
are all those results put together

Answer 21

ohk how to express arc length differential

Answer 22

@electrokid would u like to go ahead and help me understand this problem

Answer 23

proceed with your attemts. I can verfy em for ya

Answer 24

i am sorry, i know this is my prblem, but i really get confused with word problems. I simply cant do it...i would really appreciate if u can help me out with this and 1 more problem