How High is the Sea Cliff Based on Sound Travel Time?

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Homework Help Overview

The problem involves determining the height of a sea cliff based on the time it takes for a rock to fall and the sound of it hitting the ocean to travel back up. The subject area includes kinematics and sound propagation.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the height of the cliff and the time taken for the rock to fall and for the sound to travel back. They explore equations related to free fall and sound travel, questioning how to manipulate these equations to find the height.

Discussion Status

Some participants have suggested setting up equations based on the time variables involved, while others are clarifying the steps needed to isolate variables. There is an ongoing exploration of how to combine the equations effectively, but no consensus has been reached on a specific method.

Contextual Notes

The discussion is constrained by the requirement to use the given total time of 4 seconds and the speed of sound, as well as the gravitational constant for the calculations.

dwilson89
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Please help! I've been both conceptually blocked for quite some time and need help fast!
A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 4.0 later. Given the speed of sound is 340m/s, calculate how high the cliff is in meters.
 
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If h is the height of the cliff, time taken by the rock to fall is given by

h = 1/2*g*t1^2.

Time taken by the sound to reach the top of the cliff is t2 = h/340.

Now t1 + t2 = 4 s.

Substitute the values of t1 and t2 in the above equations and solve for h.
 
rl.bhat said:
If h is the height of the cliff, time taken by the rock to fall is given by

h = 1/2*g*t1^2.

Time taken by the sound to reach the top of the cliff is t2 = h/340.

Now t1 + t2 = 4 s.

Substitute the values of t1 and t2 in the above equations and solve for h.





So do you mean solve to T1 in the first equation, then add the two together and solve for h?
 
Get t1 in terms of h. Then get t2 in terms of h.
& Substitute these into t1 + t2 = 4.
 

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