Projectile Motion w/o Horizontal Givens

[Penguin'15]

Homework Statement

A soccer player kicks a rock horizontally off a 40.0m-high cliff into a pool of water. If the player hear the sound of the splash 3.00s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343 m/s.

I wrote down givens in the y-direction:
ΔY = -40.0m
t = 3.00s
a = -9.80m/s^2
Vo = 0
θ = 0°

And in the x-direction:
a = 0
t = 3.00s

Homework Equations

ΔY=v0t+(1/2)at2
v=v0+at

The Attempt at a Solution

I am assuming that the intial y-velocity is equal to 0, since the rock was kicked horizontally...is that correct? That means I am looking for the initial velocity in the x-direction. However, I am not given displacement in the x-direction. So how do I set up the problem? Also, is the speed of sound important?

Thank you for your help!

 

[TSny]

Hello Penguin'15 and welcome to PF!

Yes, the initial y-component of velocity is zero.

If t = 0 is the time the rock was kicked, can you find the time t at which the rock lands in the water?

Then think about how you can use this time.

 

[Penguin'15]

Time is given in the problem as 3.00s. The speed of sound is minimal, and not much use until I know how far the rock actually traveled.
How can I use this time to find the x-displacement and/or inital velocity in the x direction?

 

[TSny]

From the information given, you can calculate the time it takes for the rock to land in the water. You will see that it is not 3.00 s. The difference represents the time it takes for the sound of the splash to reach the soccer player, which will be important in determining the x-displacement of the rock.

 

[SteamKing]

343 m/s is a pretty fast clip.

 

[Penguin'15]

Oh I get it now! I was really confused for a sec, but it makes sense. Thank TSny!