Answer:
=6.5%
Explanation:
Mass of the ball:
]
Initial velocity of the ball: ![v_{i1}](https://tex.z-dn.net/?f=v_%7Bi1%7D)
final velocity of the ball:
which is -30/100 of
=![-0.3v_{i1}](https://tex.z-dn.net/?f=-0.3v_%7Bi1%7D)
Mass of the bottle: ![m_{2} =2.4kg](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D2.4kg)
Initial velocity of the bottle: ![v_{i2}=0m/s](https://tex.z-dn.net/?f=v_%7Bi2%7D%3D0m%2Fs)
final velocity of the bottle:
is unknown (to find)
<em>by using conservation momentum, which stated that the initial momentum is equal to the final momentum.</em>
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<em>so since the bottle is at rest firstly, therefore </em>
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<em> </em><em>equation 1</em>
so now substitute
into equation 1
![m_{1} v_{i1} =m_{1} (-0.3v_{i1} ) +m_{2} v_{f2}](https://tex.z-dn.net/?f=m_%7B1%7D%20v_%7Bi1%7D%20%20%3Dm_%7B1%7D%20%28-0.3v_%7Bi1%7D%20%29%20%2Bm_%7B2%7D%20v_%7Bf2%7D)
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<em>collect the like terms</em>
![m_{1} v_{i1} +0.3m_{1}v_{i1} =m_{2} v_{f2}](https://tex.z-dn.net/?f=m_%7B1%7D%20v_%7Bi1%7D%20%20%20%2B0.3m_%7B1%7Dv_%7Bi1%7D%20%20%3Dm_%7B2%7D%20v_%7Bf2%7D)
![1.3m_{1} v_{i1} =m_{2} v_{f2}](https://tex.z-dn.net/?f=1.3m_%7B1%7D%20v_%7Bi1%7D%20%20%20%3Dm_%7B2%7D%20v_%7Bf2%7D)
divide both side by ![m_{2}](https://tex.z-dn.net/?f=m_%7B2%7D)
![v_{f2}=\frac{1.3m_{1} v_{i1}}{m_{2} }](https://tex.z-dn.net/?f=v_%7Bf2%7D%3D%5Cfrac%7B1.3m_%7B1%7D%20v_%7Bi1%7D%7D%7Bm_%7B2%7D%20%7D)
Now substitute
![v_{f2} =\frac{1.3*0.12*v_{i1}}{2.4}\\v_{f2} =\frac{0.156v_{i1} }{2.4} \\v_{f2} =0.065v_{i1}](https://tex.z-dn.net/?f=v_%7Bf2%7D%20%3D%5Cfrac%7B1.3%2A0.12%2Av_%7Bi1%7D%7D%7B2.4%7D%5C%5Cv_%7Bf2%7D%20%20%20%20%3D%5Cfrac%7B0.156v_%7Bi1%7D%20%7D%7B2.4%7D%20%5C%5Cv_%7Bf2%7D%20%3D0.065v_%7Bi1%7D)
6.5%![v_{i1}](https://tex.z-dn.net/?f=v_%7Bi1%7D)
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Answer:
D.Entropy tends to increase.
Explanation:
The second of thermodynamics states that the state of entropy of the entire universe,as an isolate system, will always increase over time
The most widely accepted scientific explanation of the origin of the universe is D. The big bang theory.