Question

A revolving search light, which is 800 yards from the shore, makes 2 revolutions (4
radians) per minute. How fast is the light traveling along the straight beach when it
is 1000 yards from the lighthouse?

HELP

Answer 1

is this a calculus problem?

Answer 2

yea

Answer 3

what topic is it in ?

Answer 4

thats what i was thinking .....because its right off the final review

Answer 5

damn you are typing a lot rob O.o

Answer 6

is this calc 1 mmonish91 ?

Answer 7

yes

Answer 8

sorry... i can't think of the topic this question involves

Answer 9

thanks for your help though

Answer 10

Imagine a rigid rod 1000 yards long, attached to the searchlight rotating @ 2 revolutions per minute or 120 revolutions per hour.
The circumference of a circle of radius 1000 is 2000 Pi.
Multiply 2000 Pi by 120 revolutions per hour and by 3 to convert to feet.
2000 * Pi * 120 * 3 = 720000 Pi feet /hr
The tip of the rod travels (720000 Pi)/5280 or 428.4 miles per hour over the beach in a circular motion.

I hope I got this right.

Answer 11

hmm.. interesting

Answer 12

\(\cos \theta = y/800\). We want to find \(dy/dt\) when \(y=1000\).
Take the derivative implicitly we have
\(-\sin\theta \cdot d\theta/dt=1/800\cdot dy/dt\qquad(*)\)
When \(y=1000\) the opposite side of the angle theta is \(\sqrt{1000^2-800^2}=360\).
In that case \(\sin\theta = 360/1000=3.6\)
plug in \(\sin \theta =3.5\) and \(y=1000\) to \((*)\) we have
\(-3.6\cdot 4\pi=1/800\cdot dy/dt\)
\(dy/dt=-3.6\cdot 4\pi\cdot 800\) yards/minute.

Answer 13

Sorry the length of the opposite side should be \(600\) and \(\sin \theta =0.6\)
So the answer is
\(dy/dt=-0.6\cdot 4\pi\cdot 800\)

Answer 14

@watchmath-\[\cos 4\pi = 800/y\cosine is adjacent over hyp

Answer 15

That is correct. The y is the hypothenuse, the 800 is the adjacent.

Answer 16

yes, so the one that i gave is correct?

Answer 17

The theta is also changing with respect to t. So we can only say that
\(\cos(\theta)=y/800\)

Answer 18

but, we are talking here with the cosine.

Answer 19

what are you trying to say about cosine function?

Answer 20

cosine is adjacent over hypothenuse

Answer 21

The \(4\pi\) is the rate of how the theta changes, i.e., \(d\theta/dt=4\pi\) and not an actual angle itself.

Answer 22

I agree with you, what I didn't agree is that you plug in \(4\pi\) for the angle.

Answer 23

yeah..i don't have problem with that.

Answer 24

i'm sorry, it must be no 4.

Answer 25

Ah I see... what you meant now ....yes. I should write 800/y instead of y/800. I didn't draw the picture. I just did it in my head :D. Thanks for the correction.

Answer 26

lol, you are welcome:)

Answer 27

(Please check again pat18)
I think I have to fix this before I off go to bed
\(\cos \theta =800/y\)
\(-\sin\theta\cdot d\theta/dt=-800/y^2\cdot dy/dt\)
\(0.6\cdot 4\pi=800/10^6\cdot dy/dt\)
\(dy/dt=3000\pi\text{ yards/minute}\)
(I am not good at physics, is that make sense?)

Answer 28

you are welcome.