Question

A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 4.2 s later. If the speed of sound is 340 m/s, how high is the cliff?

Answer 1

is it heard 4.2 s after releasing the rock, or after seeing it hit the water?

Answer 2

it is heard 4.2 s after releasing the rock

Answer 3

hmm, then we would need to develop a gravity model i spose

Answer 4

all I know is g=9.80 m/s^2

Answer 5

I switched into the class a week late so i am behind on these problems

Answer 6

hmm, h(t) = -4.9 t^2 + h would be the falling equation

Answer 7

how did you get -4.9?

Answer 8

9.8/2

Answer 9

do you know how to work calculus?

Answer 10

i am taking calculus this year

Answer 11

well, what you may learn is:

acceleration, integrates to velocity, integrates to distance

as such, if

a = k
v = kt + c
s = kt^2/2 +ct + d

since we know k=-9.8 (its a downward force), and the initial velocity is 0, so c=0. the d is the only unknown

Answer 12

now, we know the total time it takes is 4.2 seconds ..... and the height going down is the same as it coming up

then we can start to equate things and hopefully it all works out

Answer 13

so plug 4.2 into t?

Answer 14

lets try:

d = -4.9t^2 and d = 340t

the time it takes to fall is not the same time it takes for the sound to get there so we cant just plug in 4.2

Answer 15

im thinking the negative is not going to be proper here.

so lets try: 4.9t^2 = 340t

4.9t^2 - 340t = 0

t(4.9t - 340) = 0, since t=0 is not going to be it then t=340/4.9 maybe

Answer 16

somethings not setting right with that to me

Answer 17

That would lead t to equal 69.39

Answer 18

yeah ... trying to see what the flaw is if any

logically, the distance it takes the rock to fall is the same distance it takes for the sound to travel back, maybe using the same t parameter is a bad idea and we need

distance to fall = 4.9 a^2
distance back = 340 b

such that a+b = 4.2

Answer 19

this is a system of equations that may be solvable

Answer 20

a+b = 4.2; b=4.2-a

4.9a^2 - 340b = 0

4.9a^2 - 340(4.2-a) = 0

now its a quadratic in a

Answer 21

a = 3.97256 according to the wolf, for speed of a solution that is

Answer 22

so is that the answer?

Answer 23

thats what the value of a is, the answer should be d=4.9a^2

Answer 24

or d = 340(4.2-a)

Answer 25

d=77.23

Answer 26

or 78.2

Answer 27

im getting about 77.33

Answer 28

ok ill try all 3

Answer 29

ok i got it!!!! thanks so much for the help

Answer 30

:) youre welcome, that was kinda fun .... at least it made me think more than usual

Answer 31

yes it is a very challenging high school course!