Answer:
So the time it takes the first stone to fall from the top of the cliff is 3.88 seconds.
Explanation:
We can use free fall equations to describe the motion of both stones given by
Once we have set both systems we can then solve for the time of the first stone.
Setting up free fall equations.
For the first stone, we do not know about the its initial height, nor its time, but we know it is being falling from rest so its initial velocity is 0, thus the equation that describes it will be:
Now at the bottom or ground level we will have y = 0, thus we will have
For the second stone, we know its take is 3.9 seconds past the initial time of the first stone so we will have
which means
It has also an initial speed, but aiming downwards so . Using the given information we can write
At the bottom or ground level we have y = 0
Thus we get a system of 2 equations and 2 unknowns that are the initial height and the initial time t.
Solving the system of equations
We can solve for the height of the cliff from the first equation and plug it on the second equation.
Replacing on the second equation we get
At this point we can plug the value of the gravity and expand it in order to simplify it.
Combining like terms we get
t = 3.88s
So the time it takes the first stone to fall from the top of the cliff is 3.88 seconds.