Question

A lighthouse is located on a small island,
4 kms away from the nearest point P on a
straight shoreline, and its light makes six rev-
olutions per minute. How fast is the beam of
light moving along the shoreline when it is 3
kms from P ?

Answer 1

da/dt = 12pi per minute, i can see that much at least

Answer 2

dP/dt = dP/da * da/dt

Answer 3

What is the relation of the angle to the distance ?

Answer 4

huh?

Answer 5

tan(a)=P/4 right?

Answer 6

Yeppp

Answer 7

and do the tangent inverse

Answer 8

of 3/4?

Answer 9

well, at that instant it is 3/4 ; but in general

Answer 10

tan(a) = P/4

sec^2(a) da/dt = 1/4 dP/dt

Answer 11

dP/dt = 4 sec^2(a) da/dt

Answer 12

dP/dt = 4 sec^2(a) 12pi

dP/dt = 44pi sec^2(a)

what is the angle of tan-1(3/4) ?

Answer 13

dP/dt = 44pi sec^2(tan^(-1)(3/4)) = 215.98 units per hour

maybe?

Answer 14

hmm

Answer 15

prolly not tho

Answer 16

noo. not close either

Answer 17

ive never been able to get a handle on the lighthouse one fer some reason

Answer 18

1. 4488pi kms/h
2. 4504pi kms/h
3. 449pi kms/h
4. 4500pi kms/h
5. 4501pi kms/h

Answer 19

oh, my units are in minutes

Answer 20

and the pi is estimated

Answer 21

(275 pi)/4; per minute

60(275 pi)/4 = 4125pi per hour

Answer 22

...... harumph

Answer 23

4500 .... 4*12 = 48

Answer 24

dP/dt = 48pi sec^2(tan^(-1)(3/4)) = 75pi /min

75*60 = 4500pi / hr

Answer 25

omg thxxxx!