# Tricky 2d motion question

A soccer player kicks a rock horizontally off a cliff 38.2m high into a pool of water. If the player hears the sound of the splash 3.13s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343m/s

What I dont understand here is, determining the horizontal displacement to determine the initial horizontal velocity.

1) I determine the time it take the rock to fall to the pool using Viy = 0.0 m/s and using
deltax= vit +1/2at^2
2) determine the time it takes for the sound to reach the ears by subtracting 3.13-2.792 (time for rock to fall) = 0.338 s
3) now i need to determine the horizontal displacement of the rock, Dont understand how to do that.

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Nugatory
Mentor
What was the distance from the player to the splash? You have enough information to work that out, and once you do you can draw a triangle and the Pythagorean theorem will get you home from there.

462chevelle
Gold Member
D=At. so I would think you would need to mass of the object to calculate the velocity on the y axis using g so you would determine which time was taking on the y axis and which time on the x axis. not a physics guru but now you have me trying to solve this one. is that the question word for word? nothing taken out? displacement to y axis is D=1/2at^2. its accelerating on the y axis at -9.8 ms^2 but still don't know the time cause we don't have the mass

Try drawing a diagram of the sound returning to the kicker, treating the sound as a 'projectile.' (Edit: Assuming a straight line from source to the kicker) You have a speed and a time for the sound returning. My mental image (and gut) shows that it becomes a geometry problem at that point, seeing as you have the information about the vertical displacement already.

Edit: looks like I'm a bit late but my solution is in line with post #2. Not sure if you can do it any other way.

Bobbywhy
Gold Member
Wouldn't kicking a rock hurt the soccer player's foot?

Let the velocity be v. then the horizontal distance is D = v*(t=2.792).
Then, apply the pythagorean theorem sqrt(D^2 + h^2) = 343*0.338.
height of the cliff (known).

sudu is correct.

You know the acceleration of gravity and the vertical height that the rock falls, so you know the time it took for the rock to fall.
You know that the time period from the kick to hearing the splash includes both the fall time and the time for the splash sound to return.
Knowing the speed of sound and the time from the splash to hearing it, you know the distance from the kicker to the splash.
Knowing that distance (the hypotenuse) and one of the sides (*the vertical height), you can know the other side (the horizontal distance).
Knowing the horizontal distance and the fall time, you can determine the initial speed of the rock.

*I'm assuming that the problem uses a soccer player so he can kick the rock and follow through by falling down so that his ear is at the edge of the cliff at the kick point so that the vertical component of the path of the sound back to him from the splash matches the actual height of the rock's fall to the water... and he stays down until he hears it.
Otherwise, you would need to take into account and add his height, which is not provided.

Thank you all for your replys. I understand how to solve the question, I would like some more insight as to why you would assume the speed of the sound multiplied by the time for sound to travel up to be the hypotenuse. In my head I, imagine sound waves moving directly up, hence my confusion.

gneill
Mentor
Thank you all for your replys. I understand how to solve the question, I would like some more insight as to why you would assume the speed of the sound multiplied by the time for sound to travel up to be the hypotenuse. In my head I, imagine sound waves moving directly up, hence my confusion.
"Directly up" from where? Where is the sound formed? Where is it observed? What's the path from one to the other?

Sound travels radially in all directions; the direction of importance here is the line between the splash point and the soccer player.
The sound of the splash originates where the rock hits the water.
The soccer player did not just push the rock over the edge of the cliff, he kicked it.
The rock did not just fall down to the water at the foot of the cliff, it traveled forward out over the water and splashed down way out in front of the cliff.
The sound has to travel both up from the water level to the cliff top, and back across the distance from the splash to the cliff - or more simply, a diagonal line from the splash point up and back to the soccer player on the cliff. That diagonal line is the distance the sound travels...