Question

Need some help

Answer 1

Suppose a car is moving clockwise along the circle 𝑥2 + (𝑦 − 1)2 = 1 and that a
person is located at the point (0, −1). If the y-coordinate of the car is changing at
the rate of −10 𝑚/𝑠 when the car is at (1, 1), find the rate at which the distance
between the car and the person is changing at that time.

Answer 2

so what are you finding?

Answer 3

Not really sure i was thinking of doing implicit differentiation this has to do with a related rates problem.


\[\frac{ d }{ dx }x^{2}+\frac{ d }{ dx }(y-1)^{2} = 1*(\frac{ d }{ dx })\]

\[2x+ \frac{ dy }{ dx }(y^{2}-2y+1) = 2y - 2 = 0 \]

\[2x+(2y-2)(\frac{ dy }{ dx }) = 0\]

\[-2x = (2y-2)\frac{ dy }{ dx }\]

\[\frac{ -2x }{ 2y-2 } = \frac{ -2x }{ 2(y-1) } = \frac{ dy }{ dx }\]

\[\frac{ dy }{ dx } = \frac{ -x }{ (y-1) }\]

Answer 4

\[\frac{ dy }{ dt } = -10m/s, \frac{ dy }{ dx } = \frac{ -x }{ (y-1) }\]

I'm assuming that we have to find dx/dt

\[\frac{ dx }{ dt } = \frac{ \frac{ dy }{ dt }*dx~dt }{ \frac{ dy }{ dx }*dx~dt }\]

\[\frac{ dx }{ dt } = \frac{ -10 }{ (\frac{ -x }{ y-1 }) } = \frac{ 10(y-1) }{ x }\]

\[\frac{ dx }{ dt } = \frac{ 10(y-1) }{ x } |_{1,1} = ?\]

something isn't right I got 0.

Answer 5

Don't know why this is wrong

Answer 6

my book is telling me to use the distance formula

Answer 7

yes the distance formula d = sqrt ( y2 - y1)^2 + (x2 - x1)^2

we need to substitute in that

Answer 8

i'm trying to figure this out. These type of problems are not my strong point I'm afraid.

Answer 9

That's what the answer said but i'm a little lost on that.

\[d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\]

so we would substitute this into the equation in the bottom?

\[x^{2}+(y-1)^{2} = 1 \]

Answer 10

now would x1 and x2 be the point be 0 and -1 ( where the person is standing?

Answer 11

well I think the person would be at (0,-1) assuming that he is stationary and the car is at (1,1)

Answer 12

hmmm.. I#m confused to be honest

Answer 13

@welshfella like apparently what I did above to find dx/dt = 0 above is right. but it was only part of the problem.

Answer 14

The answer involved taking the derivative of the distance formula and then plugging everything in..

\[d/dt \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\]

Answer 15

I'll ask the prof.. about this...but thank you for helping. me

Answer 16

ok - well i wasn't much help!!

I can do the easier related rate problems but this oen beats me at the moment.

Answer 17

i'm confused about this too.