Answer:
Probability of tunneling is ![10^{- 1.17\times 10^{32}}](https://tex.z-dn.net/?f=10%5E%7B-%201.17%5Ctimes%2010%5E%7B32%7D%7D)
Solution:
As per the question:
Velocity of the tennis ball, v = 120 mph = 54 m/s
Mass of the tennis ball, m = 100 g = 0.1 kg
Thickness of the tennis ball, t = 2.0 mm = ![2.0\times 10^{- 3}\ m](https://tex.z-dn.net/?f=2.0%5Ctimes%2010%5E%7B-%203%7D%5C%20m)
Max velocity of the tennis ball,
= 89 m/s
Now,
The maximum kinetic energy of the tennis ball is given by:
![KE = \frac{1}{2}mv_{m}^{2} = \frac{1}{2}\times 0.1\times 89^{2} = 396.05\ J](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7Dmv_%7Bm%7D%5E%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ctimes%200.1%5Ctimes%2089%5E%7B2%7D%20%3D%20396.05%5C%20J)
Kinetic energy of the tennis ball, KE' = ![\frac{1}{2}mv^{2} = 0.5\times 0.1\times 54^{2} = 154.8\ m/s](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dmv%5E%7B2%7D%20%3D%200.5%5Ctimes%200.1%5Ctimes%2054%5E%7B2%7D%20%3D%20154.8%5C%20m%2Fs)
Now, the distance the ball can penetrate to is given by:
![\eta = \frac{\bar{h}}{\sqrt{2m(KE - KE')}}](https://tex.z-dn.net/?f=%5Ceta%20%3D%20%5Cfrac%7B%5Cbar%7Bh%7D%7D%7B%5Csqrt%7B2m%28KE%20-%20KE%27%29%7D%7D)
![\bar{h} = \frac{h}{2\pi} = \frac{6.626\times 10^{- 34}}{2\pi} = 1.0545\times 10^{- 34}\ Js](https://tex.z-dn.net/?f=%5Cbar%7Bh%7D%20%3D%20%5Cfrac%7Bh%7D%7B2%5Cpi%7D%20%3D%20%5Cfrac%7B6.626%5Ctimes%2010%5E%7B-%2034%7D%7D%7B2%5Cpi%7D%20%3D%201.0545%5Ctimes%2010%5E%7B-%2034%7D%5C%20Js)
Thus
![\eta = \frac{1.0545\times 10^{- 34}}{\sqrt{2\times 0.1(396.05 - 154.8)}}](https://tex.z-dn.net/?f=%5Ceta%20%3D%20%5Cfrac%7B1.0545%5Ctimes%2010%5E%7B-%2034%7D%7D%7B%5Csqrt%7B2%5Ctimes%200.1%28396.05%20-%20154.8%29%7D%7D)
![\eta = \frac{1.0545\times 10^{- 34}}{\sqrt{2\times 0.1(396.05 - 154.8)}}](https://tex.z-dn.net/?f=%5Ceta%20%3D%20%5Cfrac%7B1.0545%5Ctimes%2010%5E%7B-%2034%7D%7D%7B%5Csqrt%7B2%5Ctimes%200.1%28396.05%20-%20154.8%29%7D%7D)
![\eta = 1.52\times 10^{-35}\ m](https://tex.z-dn.net/?f=%5Ceta%20%3D%201.52%5Ctimes%2010%5E%7B-35%7D%5C%20m)
Now,
We can calculate the tunneling probability as:
![P(t) = e^{\frac{- 2t}{\eta}}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20e%5E%7B%5Cfrac%7B-%202t%7D%7B%5Ceta%7D%7D)
![P(t) = e^{\frac{- 2\times 2.0\times 10^{- 3}}{1.52\times 10^{-35}}} = e^{-2.63\times 10^{32}}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20e%5E%7B%5Cfrac%7B-%202%5Ctimes%202.0%5Ctimes%2010%5E%7B-%203%7D%7D%7B1.52%5Ctimes%2010%5E%7B-35%7D%7D%7D%20%3D%20e%5E%7B-2.63%5Ctimes%2010%5E%7B32%7D%7D)
![P(t) = e^{-2.63\times 10^{32}}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20e%5E%7B-2.63%5Ctimes%2010%5E%7B32%7D%7D)
Taking log on both the sides:
![logP(t) = -2.63\times 10^{32} loge](https://tex.z-dn.net/?f=logP%28t%29%20%3D%20-2.63%5Ctimes%2010%5E%7B32%7D%20loge)
![P(t) = 10^{- 1.17\times 10^{32}}](https://tex.z-dn.net/?f=P%28t%29%20%3D%2010%5E%7B-%201.17%5Ctimes%2010%5E%7B32%7D%7D)
The correct answer among the choices given is option B. The energy transformation that occurs in the core of a nuclear reactor is from nuclear energy to thermal energy. In a power plant nuclear fission which involves nuclear energy to heat up water around it. This part is the core of the process.
There are many factors that determine if an aircraft can operate from a given airport. Of course the availability of certain services, such as fuel, access to air stairs and maintenance are all necessary. But before considering anything else, one must determine if the plane can physically land at an airport, and equally as important, take off.
What is the minimum runway length that will serve?
Looking at aerial views of runways can lead some to the assumption that they are all uniform, big and appropriate for any plane to land. This couldn’t be further from the truth.
A given aircraft type has its own individual set of requirements in regards to these dimensions. The classic 150’ wide runway that can handle a wide-body plane for a large group charter flight isn’t a guarantee at every airport. Knowing the width of available runways is important for a variety of reasons including runway illusion and crosswind condition.
Runways also have different approach categories based on width, and have universal threshold markings that indicate the actual width.
To learn more about runway
brainly.com/question/11553726
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