Question

an astronomical clock has 24 dials on it it the hour hand covers a complete revolution in 24 hour and the minute hand in one hour
a) how many times are they perpendicular to each other in one hour
b) how many times are they opposite to each other in 24 hour

Answer 1

@ikram002p

Answer 2

@ganeshie8

Answer 3

maby in one hour 4 times ?

Answer 4

and b
in 24 hours is
4*24 ??

Answer 5

im assuming that for a normal clock

Answer 6

no

Answer 7

http://www.orloj.com/orloj_dial_sphere.jpg

Answer 8

:)

Answer 9

i knw nothing abt this shape lol exept im leo :P

Answer 10

does anyone know it

Answer 11

virgo

Answer 12

write vector functions of hour hand wrt to time
and samething for min hand

Answer 13

dont know any of that

Answer 14

and solve for all time values where h'(t)=-1/min'(t)

Answer 15

kk well then lets use simple math

Answer 16

in 1 hour it will be perpendicular twice right

Answer 17

so in 24 hrs u will see it perpendicular 48 times

Answer 18

thats it ?

Answer 19

wait it only asks you perpendicular for 1 hour though

Answer 20

so ya thats it

Answer 21

http://www.wolframalpha.com/input/?i=2pi*cos%282pix%29*pi%2F12*%28cos%28pi*x%2F12%29%29+%3D+-1%2C+0%3C+x%3C1

Answer 22

are you sure

Answer 23

now how many times would it be opposite each other in 24 hrs

Answer 24

lol ganeshi

Answer 25

ganeshi what is it your freaking me breo

Answer 26

what is this meaning of this wolfram!

Answer 27

wolfram is giving up..
so we need to count manually how many solutions will be there i gueess..

Answer 28

×_×

Answer 29

those equations look okay @dan815 @ikram002p ?

Answer 30

dnt ask me i knw nothing,
i dnt knw this clock sys :o

Answer 31

http://www.enotes.com/homework-help/how-many-times-will-minute-hand-hour-handa-433164

Answer 32

complete failure!

Answer 33

Hours dial :
1 revolution every 24 hours, so 1/24 revolutiosn every hour :
y1 = sin(pi/12t)

Minutes dial :
1 revolution every 1hours, so 1 revolutiosn every hour :
y1 = sin(2pit)

Answer 34

oh u want a vector function ?

Answer 35

that was the other way

Answer 36

why exams r tough these days -.-

Answer 37

i thought of the most trivial answers when he shut down my vector ideas :)

Answer 38

complete mistake

Answer 39

Hours :
y1 = sin(pi/12t) i + cos(pi/12t) j

Minutes :
y2 = sin(2pit) i + cos(2pit) j

Answer 40

there are ur vector functions,
if they're right, i guess we can simply solve for y1'*y2' = -1 ?

Answer 41

unless our reasoning is flawed... lol

Answer 42

it must be fine solving that for t=0 to 24

Answer 43

for part a)
0<=t<=1

right ?

Answer 44

or any other interval of length 1

Answer 45

oh yes

Answer 46

wait does t=0 to t=1 complete a full day in these functions of yours

Answer 47

t is in hours

Answer 48

revolutions per hour it is..

Answer 49

starting at 6:6 position on a 24 hour clock
hour hand
r(t)=<cos(2pit),sin(2pi t)>

min hand
r2(t)=<cos(24*24*2pi t),sin(24*24*2pi t)>

Answer 50

@ganeshie8 u think that works? 24* 24

Answer 51

no 24*

Answer 52

just 1 24

Answer 53

hour hand covers a complete revolution in 24 hours

Answer 54

hour hand
r(t)=<cos(2pit),sin(2pi t)>

Answer 55

how does this complete 1 revolution in 24 hours ?

Answer 56

in t=0 to t=1

Answer 57

you also using unit as hour right ?

Answer 58

oh you're using unit as day ?

Answer 59

then it makes sense to meh.. .

Answer 60

r(t)=<cos(2pi t),sin(2pi t)>
r2(t)=<cos(24*2pi t),sin(24*2pi t)>

t=0 to t=1
ya for 1 fll day

Answer 61

yah this looks good.. .

Answer 62

but, wat does it mean to multiply two vectors ?

Answer 63

we wont multiply

Answer 64

r'(t) * r2'(t)

Answer 65

uhmm

Answer 66

we will get the slope functions both both and see all the time values they are perpendicular

Answer 67

r(t)=<cos(2pi t),sin(2pi t)>
r2(t)=<cos(24*2pi t),sin(24*2pi t)>

r'(t) = 2pi<-sin(2pit) , cos(2pit) >
r2'(t)=48pi<-sin(24*2pi t),cos(24*2pi t)>

Answer 68

okay so
for t from 0 to 1
r'(t) dot r2(t)==0
return t

Answer 69

lol

Answer 70

if only the computer was smart enough to understand that

Answer 71

man ive been learning about circuits and gates.. its so amazing i feel like i can build those little computers people are making on minecraft soon

Answer 72

oh we will take the dot product and set it equal to 0

Answer 73

yah

Answer 74

oh nice, digital electronics or vlsi ?

Answer 75

i dunno its just a intro course EECS

Answer 76

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/lecture-8/

Answer 77

pretty much a copy of that course

Answer 78

ohh u must be having fun :) digital part is easy, but analog design is a bit tough :o

Answer 79

yeah

Answer 80

its fun

Answer 81

that prof on mit guy is really cool too

Answer 82

lets oslve this i want to see what it comes out to

Answer 83

Anant Agrawal... indian guy lol

Answer 84

yeah haha

Answer 85

best teacher!