According to the conservation of momentum. In this situation, the initial momentum is equal to zero.
Since,
p=mv (Momentum)
The initial velocity of the ball = 0 m/s
The initial velocity of the man = 0 m/s
Therefore,
Total Momentum = 0
Law of Conservation of momentum states that the vector sum of the final momenta must be equal to zero which means they will have the same magnitude but in opposite directions.
<span>When the ball is kicked forward along the surface with a speed 15 m/s.
</span>then the momentum will be:
p = 4 x 15 = 60 kgm/s.
Now, the momentum of the man can be calculated as:
p = 60 kgm/s
mv = 60 kgm/s
As,
mass of the man = 80kg
So,
80 × v = 60 kgm/s
v = 60÷80
v = 0.75 m/s
What is your question can you show pictures?
Answer: The height of rollercoaster cart above the ground is 1.53 m.
The velocity of rollercoaster cart is 5.29 m/s.
Explanation:
Potential energy is the energy occupied by a substance due to its position. Formula for potential energy is as follows.
P.E = mgh
where,
m = mass of substance
g = gravitational constant = ![9.8 m/s^{2}](https://tex.z-dn.net/?f=9.8%20m%2Fs%5E%7B2%7D)
h = height
Substitute the values into above formula as follows.
![P.E = m \times g \times h\\67500 J = 4500 kg \times 9.8 m/s^{2} \times h\\h = \frac{67500 J}{4500 kg \times 9.8 m/s^{2}}\\= 1.53 m](https://tex.z-dn.net/?f=P.E%20%3D%20m%20%5Ctimes%20g%20%5Ctimes%20h%5C%5C67500%20J%20%3D%204500%20kg%20%5Ctimes%209.8%20m%2Fs%5E%7B2%7D%20%5Ctimes%20h%5C%5Ch%20%3D%20%5Cfrac%7B67500%20J%7D%7B4500%20kg%20%5Ctimes%209.8%20m%2Fs%5E%7B2%7D%7D%5C%5C%3D%201.53%20m)
Hence, the height of rollercoaster cart above the ground is 1.53 m.
Kinetic energy is the energy occupied by the motion of a substance. Formula for kinetic energy is as follows.
![K.E = \frac{1}{2}m \times v^{2}](https://tex.z-dn.net/?f=K.E%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm%20%5Ctimes%20v%5E%7B2%7D)
where,
m = mass of substance
v = velocity of substance
Substitute the values into above formula as follows.
![K.E = \frac{1}{2}m \times v^{2}\\63000 J = \frac{1}{2} \times 4500 kg \times v^{2}\\v^{2} = \frac{63000 J \times 2}{4500 kg}\\v = 5.29 m/s](https://tex.z-dn.net/?f=K.E%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm%20%5Ctimes%20v%5E%7B2%7D%5C%5C63000%20J%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%204500%20kg%20%5Ctimes%20v%5E%7B2%7D%5C%5Cv%5E%7B2%7D%20%3D%20%5Cfrac%7B63000%20J%20%5Ctimes%202%7D%7B4500%20kg%7D%5C%5Cv%20%3D%205.29%20m%2Fs)
Hence, the velocity of rollercoaster cart is 5.29 m/s.
Answer:
<em>There must be added 500 cm3 of alcohol to bring the concentration to 80%.</em>
Explanation:
<u>Concentration</u>
The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solution.
In the container, there are 2 liters (2000 cubic centimeters) of a solution, 75% of which is alcohol (solute) and 25% of water (solvent).
The original amount of alcohol is:
H = 2000*75% = 1500 cc
The original amount of water is:
W = 2000*25% = 500 cc
When we add x cc of pure alcohol, there are 1500+x cc of alcohol out of 2000+x cc of solution.
The new concentration is calculated as:
![\displaystyle \frac{1500+x}{2000+x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1500%2Bx%7D%7B2000%2Bx%7D)
And it's known this concentration is 80% (0.8), thus:
![\displaystyle \frac{1500+x}{2000+x}=0.8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1500%2Bx%7D%7B2000%2Bx%7D%3D0.8)
Multiplying by 2000+x:
![1500+x = 0.8(2000+x)](https://tex.z-dn.net/?f=1500%2Bx%20%3D%200.8%282000%2Bx%29)
Operating:
![1500+x = 1600+0.8x](https://tex.z-dn.net/?f=1500%2Bx%20%3D%201600%2B0.8x)
Rearranging:
![x-0.8x=1600-1500](https://tex.z-dn.net/?f=x-0.8x%3D1600-1500)
![0.2x=100](https://tex.z-dn.net/?f=0.2x%3D100)
![x=100/0.2](https://tex.z-dn.net/?f=x%3D100%2F0.2)
x= 500
There must be added 500 cm3 of alcohol to bring the concentration to 80%