Earth Questions


QHow long (in hours) does it take for the water to fall a distance d/4 from its highest level?

On a given port , the tides cause the ocean surface to rise and fall a distance d (from highest level to the lowest level ) in simple harmonic motion with a period of 11.5 hours. How long ( in hours ) it takes for the water to fall a distance d / 4 its highest level ?

1 answers

This question still have no answer summary yet.
#1AnonymousAnswered at 2013-05-12 18:48:43
Assuming that at time t = 0 corresponds to a ridge, the equation:

h = ( d / 2 ) cos ( 2πt / 11.5 )

gives the height of the tide above / below average at time t in hours. The peak is at d / 2, so you want to solve
h = d / 2 - d / 4 = d / 4
( d / 2 ) cos ( 2πt / 11.5 ) = d / 4
cos ( 2πt / 11.5 ) = 1/2
The smallest positive value of t also gives the smallest positive argument of the cosine possible , so that the inverse cosine gives the answer directly :
2πt / 11.5 = cos ⁻ ¹ ( 1/2 ) = π / 3
t = 11.5 / 6 .... after multiplying both sides by 11.5 / ( 2π )
t = 23 /12 hour or 1 hour and 55 minutes
Anonymous Sign In Sign Up
Add Answer of
How long (in hours) does it take for the water to fall a distance d/4 from its highest level?

Did this answer your question? If not, ask a new question.

Related Answers