Answer:
![v_{2f} = \frac{2vm_1}{m_2 + m_1}](https://tex.z-dn.net/?f=v_%7B2f%7D%20%3D%20%5Cfrac%7B2vm_1%7D%7Bm_2%20%2B%20m_1%7D)
Explanation:
If the collision is elastic and exactly head-on, then we can use the law of momentum conservation for the motion of the 2 balls
Before the collision
![P_i = m_1v](https://tex.z-dn.net/?f=P_i%20%3D%20m_1v)
After the collision
![P_f = m_1v_{1f} + m_2v_{2f}](https://tex.z-dn.net/?f=P_f%20%3D%20m_1v_%7B1f%7D%20%2B%20m_2v_%7B2f%7D)
So using the law of momentum conservation
![P_i = P_f](https://tex.z-dn.net/?f=P_i%20%3D%20P_f)
![m_1v = m_1v_{1f} + m_2v_{2f}](https://tex.z-dn.net/?f=m_1v%20%3D%20m_1v_%7B1f%7D%20%2B%20m_2v_%7B2f%7D)
We can solve for the speed of ball 1 post collision in terms of others:
![v_{1f} = v - v_{2f}\frac{m_2}{m_1}](https://tex.z-dn.net/?f=v_%7B1f%7D%20%3D%20v%20-%20v_%7B2f%7D%5Cfrac%7Bm_2%7D%7Bm_1%7D)
Their kinetic energy is also conserved before and after collision
![m_1v^2/2 = m_1v_{1f}^2/2 + m_2v_{2f}^2/2](https://tex.z-dn.net/?f=m_1v%5E2%2F2%20%3D%20m_1v_%7B1f%7D%5E2%2F2%20%2B%20m_2v_%7B2f%7D%5E2%2F2)
![m_1v^2 = m_1v_{1f}^2 + m_2v_{2f}^2](https://tex.z-dn.net/?f=m_1v%5E2%20%3D%20m_1v_%7B1f%7D%5E2%20%2B%20m_2v_%7B2f%7D%5E2)
From here we can plug in ![v_{1f} = v - v_{2f}\frac{m_2}{m_1}](https://tex.z-dn.net/?f=v_%7B1f%7D%20%3D%20v%20-%20v_%7B2f%7D%5Cfrac%7Bm_2%7D%7Bm_1%7D)
![m_1v^2 = m_1\left(v - v_{2f}\frac{m_2}{m_1}\right)^2 + m_2v_{2f}^2](https://tex.z-dn.net/?f=m_1v%5E2%20%3D%20m_1%5Cleft%28v%20-%20v_%7B2f%7D%5Cfrac%7Bm_2%7D%7Bm_1%7D%5Cright%29%5E2%20%2B%20m_2v_%7B2f%7D%5E2)
![m_1v^2 = m_1\left(v^2 - 2vv_{2f}\frac{m_2}{m_1} + v_{2f}^2\frac{m_2^2}{m_1^2}\right) + m_2v_{2f}^2](https://tex.z-dn.net/?f=m_1v%5E2%20%3D%20m_1%5Cleft%28v%5E2%20-%202vv_%7B2f%7D%5Cfrac%7Bm_2%7D%7Bm_1%7D%20%2B%20v_%7B2f%7D%5E2%5Cfrac%7Bm_2%5E2%7D%7Bm_1%5E2%7D%5Cright%29%20%2B%20m_2v_%7B2f%7D%5E2)
![m_1v^2 = m_1v^2 - 2vv_{2f}m_2 + v_{2f}^2\frac{m_2^2}{m_1} + m_2v_{2f}^2](https://tex.z-dn.net/?f=m_1v%5E2%20%3D%20m_1v%5E2%20-%202vv_%7B2f%7Dm_2%20%2B%20v_%7B2f%7D%5E2%5Cfrac%7Bm_2%5E2%7D%7Bm_1%7D%20%2B%20m_2v_%7B2f%7D%5E2)
![v_{2f}^2(m_2 + \frac{m_2^2}{m_1}) - 2vm_2v_{2f} = 0](https://tex.z-dn.net/?f=v_%7B2f%7D%5E2%28m_2%20%2B%20%5Cfrac%7Bm_2%5E2%7D%7Bm_1%7D%29%20-%202vm_2v_%7B2f%7D%20%3D%200)
![v_{2f}(1 + \frac{m_2}{m_1}) = 2v](https://tex.z-dn.net/?f=v_%7B2f%7D%281%20%2B%20%5Cfrac%7Bm_2%7D%7Bm_1%7D%29%20%3D%202v)
![v_{2f} = \frac{2v}{1 + \frac{m_2}{m_1}} = \frac{2v}{\frac{m_1 + m_2}{m_1}} = \frac{2vm_1}{m_2 + m_1}](https://tex.z-dn.net/?f=v_%7B2f%7D%20%3D%20%5Cfrac%7B2v%7D%7B1%20%2B%20%5Cfrac%7Bm_2%7D%7Bm_1%7D%7D%20%3D%20%5Cfrac%7B2v%7D%7B%5Cfrac%7Bm_1%20%2B%20m_2%7D%7Bm_1%7D%7D%20%3D%20%5Cfrac%7B2vm_1%7D%7Bm_2%20%2B%20m_1%7D)
Answer: the correct answer is (B) He did not know that interstellar dust made it hard from him to see a large part of the Milky Way's disk.
Explanation:
We live in a dusty Galaxy. Because interstellar dust absorbs the light from stars, Herschel could see only those stars within about 6000 light-years of the Sun.
Answer:
The mass of the solution is 120 g.
Explanation:
The mass of the solution is given by:
![m_{sol} = m_{1} + m_{2}](https://tex.z-dn.net/?f=%20m_%7Bsol%7D%20%3D%20m_%7B1%7D%20%2B%20m_%7B2%7D%20)
Where:
: is the mass of the solution
: is the mass of the solvent
: is the mass of the solute
In the solution, the solvent is the majority compound (in mass) and the solute is the minority (in mass), so the solvent is the water and the solute is sodium chloride.
Hence, the mass of the solution is:
I hope it helps you!
Answer:
The magnitude of change in momentum is (2mv).
Explanation:
The momentum of an object is given by the product of mass and velocity with which it is moving.
Let the mass of ball is m. A tennis player smashes a ball of mass m horizontally at a vertical wall. The ball rebounds at the same speed v with which it struck the wall.
Initial speed of the ball is v and final speed, when it rebounds, is (-v). The change in momentum is given by :
p = final momentum - initial momentum
![p=-mv-mv\\\\p=-2mv](https://tex.z-dn.net/?f=p%3D-mv-mv%5C%5C%5C%5Cp%3D-2mv)
So, the magnitude of change in momentum is (2mv).