Why is it hard to breath on top of a mountain?
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First we need to find the speed of the dolphin sound wave in the water. We can use the following relationship between frequency and wavelength of a wave:
where
v is the wave speed
its wavelength
f its frequency
Using
and 
, we get
We know that the dolphin sound wave takes t=0.42 s to travel to the tuna and back to the dolphin. If we call L the distance between the tuna and the dolphin, the sound wave covers a distance of S=2 L in a time t=0.42 s, so we can write the basic relationship between space, time and velocity for a uniform motion as:
and since we know both v and t, we can find the distance L between the dolphin and the tuna:
where
v is the wave speed
f its frequency
Using
We know that the dolphin sound wave takes t=0.42 s to travel to the tuna and back to the dolphin. If we call L the distance between the tuna and the dolphin, the sound wave covers a distance of S=2 L in a time t=0.42 s, so we can write the basic relationship between space, time and velocity for a uniform motion as:
and since we know both v and t, we can find the distance L between the dolphin and the tuna:
We can use the law of conservation of energy to solve the problem.
The total mechanical energy of the system at any moment of the motion is:
where U is the potential energy and K the kinetic energy.
At the beginning of the motion, the ball starts from the ground so its altitude is h=0 and therefore its potential energy U is zero. So, the mechanical energy is just kinetic energy:
When the ball reaches the maximum altitude of its flight, it starts to go down again, so its speed at that moment is zero: v=0. So, its kinetic energy at the top is zero. So the total mechanical energy is just potential energy:
But the mechanical energy must be conserved, Ef=Ei, so we have
and so, the potential energy at the top of the flight is
The total mechanical energy of the system at any moment of the motion is:
where U is the potential energy and K the kinetic energy.
At the beginning of the motion, the ball starts from the ground so its altitude is h=0 and therefore its potential energy U is zero. So, the mechanical energy is just kinetic energy:
When the ball reaches the maximum altitude of its flight, it starts to go down again, so its speed at that moment is zero: v=0. So, its kinetic energy at the top is zero. So the total mechanical energy is just potential energy:
But the mechanical energy must be conserved, Ef=Ei, so we have
and so, the potential energy at the top of the flight is