Question

A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 3.2 s later. If the speed of sound is 340 m/s, how high is the cliff?

Answer 1

The right answer's 46 m. xD

Answer 2

okay, lets see.
say at t = 0, the rock is dropped.
it hits the ocean at a later time, say t1
the distance of the ocean from the cliff is given by
s = ut1+1/2 gt1^2
u = 0
so s = 1/2 * 9.8 *t1^2
say it takes t2 time for the moment the rock hit the ocean to the time you heard the sound.
the sound has to travel the same disntace s to reach you.
s = 340 t2
so we have 340 t2 = 4.9t1^2 ---------equation 1
and t1+t2 = 3.2 , or t2 = 3.2-t1 -------- equation 2
substitute the value of t2 into equation 1 and find t1.
use that to find s

Answer 3

the distance is 46.02 m

Answer 4

Would the quadratic formula be required?

Answer 5

yes use that

Answer 6

from s=s=vt2=4.9t1^2
340t2=4.9t1^2
69.39 t2=t1^2 substitute t2=3.2-t1

Answer 7

69.39 t2=t1^2
69.39 (3.2-t1 )=t1^2

Answer 8

69.39 (3.2-t1 )=t1^2
222.05-69.39t1 =t1^2

Answer 9

222.05-69.39t1 =t1^2
t1^2+69.39t1 -222.05=0 now use quadratic eq formula

Answer 10

t1=3.065sec subst this to s=4.9t1^2

Answer 11

s=4.9(3.065)^2 =46.03 meter ans

Answer 12

did you get it nubsauce?

Answer 13

Yeah, thanks for the help.