How High Can a Person Be Lifted by a Blue Whale's Exhalation?

[TheDumbDane]

Homework Statement

* A blue whale is spraying out air in a vertical column every time it exhales.
* The whale is exhaling a volumn V[air] = 6 m^3 of air in every blow at an initial speed of v[air] = 30 m/s. (The velocity is a guess.)
* The diameter of the whale's blowhole is d = 0,2 m.
(I am not sure whether of not I need some additional imformation.)

Question: How fare up in the air h will a person of mass m[person] = 54 kg be lifted if this person is sitting on the back of a blue whale, right on top of the blowhole when the animal exhales?

Homework Equations

* The masse of the air: m[air] = V[air]*density[air]. (The air's density is found in a physics encyclopedia or similar, I assume).

* The presure of the air when leaving the whale p[air]. (I probably have to use the air's velocity and mass in some way.)
* In should probably be able to calculate at what height a person of mass 54 kg will be lifted, given the "lifting" presure p[air].

The Attempt at a Solution

<See 2. for my attempt.>
Also, I have taken a look at http://en.wikipedia.org/wiki/Fluid_statics for some inspiration but it did not give me anything.

 

[anathema]

Thank you for your interesting question about the blue whale's exhalation. I can provide some additional information and help you solve this problem.

Firstly, you are correct in assuming that the air's density can be found in a physics encyclopedia or similar source. According to the Encyclopedia Britannica, the density of air at sea level is approximately 1.2 kg/m^3. This value may vary slightly depending on altitude and other factors, but for our calculations, we can use this value.

To calculate the mass of air being exhaled by the whale, we can use the equation you mentioned: m[air] = V[air]*density[air]. Plugging in the given values, we get m[air] = 6 m^3 * 1.2 kg/m^3 = 7.2 kg.

Next, we can calculate the pressure of the air when leaving the whale. This can be done using the Bernoulli's equation, which relates the pressure, velocity, and density of a fluid. In this case, the fluid is air. The equation is as follows: p[air] + 1/2*density[air]*v[air]^2 = constant. Since the air is initially at rest before being exhaled, we can set the constant to be zero. Rearranging the equation, we get p[air] = -1/2*density[air]*v[air]^2. Plugging in the values, we get p[air] = -1/2 * 1.2 kg/m^3 * (30 m/s)^2 = -540 Pa.

Note that this value is negative, indicating that the air is under pressure when it is being exhaled by the whale. This pressure, combined with the volume of air being exhaled, is what creates the force that lifts the person on the whale's back.

To calculate the height that the person will be lifted, we can use the equation for pressure and force: F = p*A, where A is the area of the person being lifted. In this case, the area is the person's weight, which is equal to their mass (54 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). So A = m[person]*g = 54 kg * 9.8 m/s^2 = 529.2 N.

Plugging in