A soccer player kicks a rock horizontally off a 37.1 m high cliff into a pool of water. If the player hears the sound of the splash 3.98 s later, and the speed of sound is 343 m/s, what was the initial speed given to the rock?
Note: This answer may seem to be long and complicated, but it is actually only 4 major steps:
- Find the time the rock spends falling
- Find the distance from the splash to the kicker
- Find the horizontal distance the rock travelled
- Find the velocity of the rock
I have tried to keep it as simple as possible and explain the reasoning behind all the steps.
This answer does not take into account air resistance or any sort of friction at all.
First we have to calculate the time taken for the rock to hit the water. To do this we rearrange some common formulae:
Substituting the first into the second we get:
Which we can rearrange to get:
Substituting the known values into the equation we get:
So we have the time taken for the rock to hit the water.
Next we need to find the time taken for the sound of the splash to reach the kicker.
Then we use the speed of sound to calculate the distance from the splash to the kicker.
We now need to know the horizontal distance the rock travelled. We use Pythagoras' Theorem to do this:
We now know the horizontal distance travelled and time taken before the rock hits the water, and it is simple to find out the velocity from this:
This seems to be quite a high value and if it is converted to km/hour it comes out as a staggering:
This makes me wonder if I have missed something in my working or if I have got one of the formulas wrong.
Then again it could just be that it is a made-up question and the values were not thought through.