Question

A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 15 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle between the beam and the line through the searchlight perpendicular to the wall is pi/4? Note that dTheta/dt=3(2pi)=6pi.

Answer 1

b= 15; tan(t) should give us a way to relate the light on the wall to the distance to the search light

Answer 2

15 miles is pretty far

Answer 3

tan(t) = wb^-1

sec^2(t) t' = w'b^-1

w' = sec^2(t) t'b

Answer 4

?

Answer 5

without having to guess at what you fail to grasp and try to teach you what you should have already been exposed to, why dont you try to express your confusion in a manner that can be communicated?

Answer 6

I apologize. I suffer from a learning disability and it takes a lot of work for me to understand this. I suppose my problem is structuring this in a way I understand.

Answer 7

ok, these rates of change problems require us to relate what we know to what we are trying to determine. in this case we need to relate the speed of the angle with the speed of the spotlight against the wall

the triangle i drew shows us all the parts and we can relate them together with the tangent function.

Answer 8

by taking the derivative of that relationship we construct an equation tat relates speeds together.

tan(t) = w/b

sec^2(t) t' = w'/b

we want to know w' so rearrange the eq to solve for w'

w' = b sec^2(t) t'

Answer 9

b = 15, t = pi/4, and t' = 6pi ; as given

Answer 10

soo

w' = 15 sec^2(pi/4) *6pi

Answer 11

w'=15*2*6pi if i see it right

Answer 12

which is 565.49?

Answer 13

180pi is all i can tell without a calculator

Answer 14

it wants it in mph

Answer 15

and what we found is in miles per minute aint it

Answer 16

60 minutes in an hour; so multiply by 60 to get hours

Answer 17

multiply 180pi * 60 ?

Answer 18

yeah, thats what it looks like to me. with any luck im reading it right

Answer 19

10,800?

Answer 20

yep

Answer 21

ill have to dbl chk my work to be sure tho

Answer 22

well that was wrong. crap.

Answer 23

do you have to keep it in pi or estimate it?

Answer 24

doesnt say.

Answer 25

you sure you got all the info correct in the post?

15 miles, pi/4 and 6pi per minute?

Answer 26

at 3 revolutions a minute yes

Answer 27

15 miles seems big to me; i want to see it as 1.5

Answer 28

its fifteen

Answer 29

then 10,800 pi is the best i can come up with :)

Answer 30

I hate webworks

Answer 31

yeah, i loathe having to work with a program