Tha atmosphere has no effect on gravity.
Keplers laws states that planets sweep areas in equal times is second
I think it should be option (b)
Answer:
9 joules of heat energy was produced
Explanation: there is no acceleration therefore its not a kinetic energy
Energy= force × distance
= 3×3
=9
Answer:
Part a)
![v = -(8.33\hat j + 9.33\hat i)\times 10^6 m/s](https://tex.z-dn.net/?f=v%20%3D%20-%288.33%5Chat%20j%20%2B%209.33%5Chat%20i%29%5Ctimes%2010%5E6%20m%2Fs)
Part b)
![E = 4.4 \times 10^{-13} J](https://tex.z-dn.net/?f=E%20%3D%204.4%20%5Ctimes%2010%5E%7B-13%7D%20J)
Explanation:
As per momentum conservation we know that there is no external force on this system so initial and final momentum must be same
So we will have
![m_1v_1 + m_2v_2 + m_3v_3 = 0](https://tex.z-dn.net/?f=m_1v_1%20%2B%20m_2v_2%20%2B%20m_3v_3%20%3D%200)
![(5 \times 10^{-27})(6 \times 10^6\hat j) + (8.4 \times 10^{-27})(4 \times 10^6\hat i) + (3.6 \times 10^{-27}) v = 0](https://tex.z-dn.net/?f=%285%20%5Ctimes%2010%5E%7B-27%7D%29%286%20%5Ctimes%2010%5E6%5Chat%20j%29%20%2B%20%288.4%20%5Ctimes%2010%5E%7B-27%7D%29%284%20%5Ctimes%2010%5E6%5Chat%20i%29%20%2B%20%283.6%20%5Ctimes%2010%5E%7B-27%7D%29%20v%20%3D%200)
![(30\hat j + 33.6\hat i)\times 10^6 + 3.6 v = 0](https://tex.z-dn.net/?f=%2830%5Chat%20j%20%2B%2033.6%5Chat%20i%29%5Ctimes%2010%5E6%20%2B%203.6%20v%20%3D%200)
![v = -(8.33\hat j + 9.33\hat i)\times 10^6 m/s](https://tex.z-dn.net/?f=v%20%3D%20-%288.33%5Chat%20j%20%2B%209.33%5Chat%20i%29%5Ctimes%2010%5E6%20m%2Fs)
Part b)
By equation of kinetic energy we have
![E = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 + \frac{1}{2}m_3v_3^2](https://tex.z-dn.net/?f=E%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm_1v_1%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dm_2v_2%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dm_3v_3%5E2)
![E = \frac{1}{2}(5 \times 10^{-27})(6\times 10^6)^2 + \frac{1}{2}(8.4 \times 10^{-27})(4 \times 10^6)^2 + \frac{1}{2}(3.6 \times 10^{-27})(8.33^2 + 9.33^2) \times 10^{12}](https://tex.z-dn.net/?f=E%20%3D%20%5Cfrac%7B1%7D%7B2%7D%285%20%5Ctimes%2010%5E%7B-27%7D%29%286%5Ctimes%2010%5E6%29%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%288.4%20%5Ctimes%2010%5E%7B-27%7D%29%284%20%5Ctimes%2010%5E6%29%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%283.6%20%5Ctimes%2010%5E%7B-27%7D%29%288.33%5E2%20%2B%209.33%5E2%29%20%5Ctimes%2010%5E%7B12%7D)
![E = 9\times 10^{-14} + 6.72 \times 10^{-14} + 2.82\times 10^{-13}](https://tex.z-dn.net/?f=E%20%3D%209%5Ctimes%2010%5E%7B-14%7D%20%2B%206.72%20%5Ctimes%2010%5E%7B-14%7D%20%2B%202.82%5Ctimes%2010%5E%7B-13%7D%20)
![E = 4.4 \times 10^{-13} J](https://tex.z-dn.net/?f=E%20%3D%204.4%20%5Ctimes%2010%5E%7B-13%7D%20J)