Question

Related Rates clock hands problem... ughhh

Answer 1

Minute hand on a clock is 8mm long and the hour hand is 4mm long. How fast is the distance betweeen the tips of the hands changing at one' o clock?

Answer 2

I know one revolution = 2pi radians

Answer 3

and the minute hand is 1/12 rpms

Answer 4

\[\theta=\frac{ \pi }{ 6 }\]

Answer 5

i can get the unknown distance between the min hand and hour hand by using law of cosines

Answer 6

\[z^2=x^2+y^2-2(x)(y)\cos\]

Answer 7

x=8 y = 4

Answer 8

\[z=\sqrt{80-32\sqrt{3}}\]

Answer 9

now I can find dz/dt

Answer 10

keep the z in terms of \(\theta\) only, dont sub the \(\theta = \pi/6\) yet

Answer 11

\[2z(\frac{ dz }{ dt} )= -2(8)(4)-\sin(\Theta)\frac{ d \theta }{ dt }\]

Answer 12

x and y are constants here right ?

Answer 13

\[\frac{ dz }{ dt }=(\frac{ 16 }{ \sqrt{80-32\sqrt{3}} })\frac{ -11\pi }{ 6 }\]

Answer 14

ya

Answer 15

here is my question though, when I take the derivative of everything, why does the
-2(m)(n) stay ?

Answer 16

http://www.mathematics.jhu.edu/brown/courses/f11/Problems/Problem3.9.46.pdf

Answer 17

what im going off of

Answer 18

\(s^2 = m^2 + h^2 - 2(m)(h) \cos\theta\)

Answer 19

you asking at this step, why \(m \) and \(h\) stick ?

Answer 20

ya the 2(m)(h)cos

Answer 21

after taking derivating with respective to time, yeah

Answer 22

so the 2(m)(n) are untouched

Answer 23

look at

\(\frac{d }{dt} 2(m)(h) \cos\theta\)

Answer 24

since \(m\) and \(h\) are lengths of hands of clock, they are constants. so we can take them out of derivative

Answer 25

its same as,

\(2(m)(h) \frac{d }{dt}\cos\theta\)

Answer 26

is this u asking or.. ..

Answer 27

is it because they are touching cosine?

Answer 28

hmm something like that, we can pull out the constant multiple out of derivative funciton

Answer 29

for example, if \(c\) is constant,

\(\frac{d}{dt} (c * t)\) = \(c * \frac{d}{dt} (t)\)

Answer 30

c = 0

Answer 31

c can be any fixed value, we can pull it out and take the derivative for just the variable

Answer 32

in this problem, the last part.... .
the logic for calculating \(\frac{d\theta}{dt} \) is interesting...

Answer 33

pi/6 - 2pi?

Answer 34

yea... it can be pi/6 + 2pi alsi... depends on whether the angle is shrinking or expanding.. .

Answer 35

*also

Answer 36

nice problem :) gtg cya