Height of a Cliff (Only time Given)

[PhysGoat]

Homework Statement

A person throws a rock off a cliff and hears the splash below 3.4 seconds later. If we know the speed of sound is equal to 340m/s how high is the cliff to the nearest metre?

Homework Equations

I've been trying to use, r = ut + 1/2at² and
v² = u² +2ar and
v= u + at

The Attempt at a Solution

I know that the height of the cliff should be around 56 m as:

r = 0 + 4.9(3.4)²

But i don't know how to factor in the time delay of the sound :(

The answer is: (Spoiler)

Spoiler

52 m

Thanks

 

[Redbelly98]

I know that the height of the cliff should be around 56 m as:

r = 0 + 4.9(3.4)²

But i don't know how to factor in the time delay of the sound :(

Welcome to PF!

Hint: it does not take 3.4 seconds for the rock to fall, it takes slightly less than that.

 

[Petkovsky]

Nice problem, i like it. You should set up a system of 2 equations. One will be the distance when the rock falls down and the other the distance when the sound comes up.
What is the relation between the two equations and what is the relation between the two times?