If a person jumps from the high building, taking a sight, and finishes uploading sight by using WeChat, what will the height of the building it requires? (WeChat Sight is the new, fun way to shoot and share your world through six second videos. Share your experiences with friends and family via chats or Moments.)
Since WeChat is a part of Chinese's daily lives, I am willing to use the knowledge of physics, which I already learned, to satisfy people's curiosities.
WeChat Sight usually lasts six second, and I assume it takes one more second to upload online. There are seven seconds in all. Using the formula of gravity, which is s = 1/2 *g*t^2, I can get s ＝ 1/2 ＊ 9.8 ＊ 7 ＊ 7 ＝ 240.1m. The height of one floor is around 4 meters. It means the building only needed to be 60 floors. People can find such a building easily.
Is 60-floor building the final answer? No, it is not. Do not ignore the air friction! In fact, the higher speed suffers larger air-friction. Using google, I was able to find the formula:
Force(Drag)= .5(density)(Velocity)^2(Constant of Drag)(Surface Area)
87.16(squareroot(0.6))(tanh(time*(0.11/(sqrt(0.6))))
Velocity(of time)=square root(2*mass*gravity constant/(density*surface area*Drag constant))*tanh(time*(square root(gravity*density*Drag Constant*Surface Area/(2*Mass))
When velocity starts from zero, ρ is the density of the fluid(yeah, air is a kind of fluid); Cd is drag coefficient, and A is cross sectional area. Set the formula as:
People can be assumed as a sphere, which has 0.6 diameter and cd is 1.0, when people are dropping down. The density(ρ) of a human is quite similar as the density of water. Using the normal density of air and simplify it, I got the new function:
When velocity starts from zero, ρ is the density of the fluid(yeah, air is a kind of fluid); Cd is drag coefficient, and A is cross sectional area. Set the formula as:
People can be assumed as a sphere, which has 0.6 diameter and cd is 1.0, when people are dropping down. The density(ρ) of a human is quite similar as the density of water. Using the normal density of air and simplify it, I got the new function:
Wolfram can graph the function that is shown above. The cute graph, which is about jumping from a building, is shown below:
By decreasing the acceleration, the speed becomes stable around 65 m/s. Take the integral of the function.
Finally, plugging 7s into the function, I got the distance is 204 meters, which are around 51 floors.
Compare with the previous calculation, the difference is more than 36 meters! Do not need to climb another 9 floors. I should thank for my calculation.
This calculation is important because it proves one truth again. Physics is completely versatile.
Thanks for your time.
By decreasing the acceleration, the speed becomes stable around 65 m/s. Take the integral of the function.
Finally, plugging 7s into the function, I got the distance is 204 meters, which are around 51 floors.
Compare with the previous calculation, the difference is more than 36 meters! Do not need to climb another 9 floors. I should thank for my calculation.
This calculation is important because it proves one truth again. Physics is completely versatile.
Thanks for your time.
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