Answer:
The final velocity of the first glider is 0.27 m/s in the same direction as the first glider
The final velocity of the second glider is 1.07 m/s in the same direction as the first glider.
0.010935 J
0.0858675 J
Explanation:
= Mass of first glider = 0.3 kg
= Mass of second glider = 0.15 kg
= Initial Velocity of first glider = 0.8 m/s
= Initial Velocity of second glider = 0 m/s
= Final Velocity of first glider
= Final Velocity of second glider
As momentum and Energy is conserved
![m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}](https://tex.z-dn.net/?f=m_%7B1%7Du_%7B1%7D%2Bm_%7B2%7Du_%7B2%7D%3Dm_%7B1%7Dv_%7B1%7D%2Bm_%7B2%7Dv_%7B2%7D)
![{\tfrac {1}{2}}m_{1}u_{1}^{2}+{\tfrac {1}{2}}m_{2}u_{2}^{2}={\tfrac {1}{2}}m_{1}v_{1}^{2}+{\tfrac {1}{2}}m_{2}v_{2}^{2}](https://tex.z-dn.net/?f=%7B%5Ctfrac%20%7B1%7D%7B2%7D%7Dm_%7B1%7Du_%7B1%7D%5E%7B2%7D%2B%7B%5Ctfrac%20%7B1%7D%7B2%7D%7Dm_%7B2%7Du_%7B2%7D%5E%7B2%7D%3D%7B%5Ctfrac%20%7B1%7D%7B2%7D%7Dm_%7B1%7Dv_%7B1%7D%5E%7B2%7D%2B%7B%5Ctfrac%20%7B1%7D%7B2%7D%7Dm_%7B2%7Dv_%7B2%7D%5E%7B2%7D)
From the two equations we get
![v_{1}=\frac{m_1-m_2}{m_1+m_2}u_{1}+\frac{2m_2}{m_1+m_2}u_2\\\Rightarrow v_1=\frac{0.3-0.15}{0.3+0.15}\times 0.8+\frac{2\times 0.15}{0.3+0.15}\times 0\\\Rightarrow v_1=0.27\ m/s](https://tex.z-dn.net/?f=v_%7B1%7D%3D%5Cfrac%7Bm_1-m_2%7D%7Bm_1%2Bm_2%7Du_%7B1%7D%2B%5Cfrac%7B2m_2%7D%7Bm_1%2Bm_2%7Du_2%5C%5C%5CRightarrow%20v_1%3D%5Cfrac%7B0.3-0.15%7D%7B0.3%2B0.15%7D%5Ctimes%200.8%2B%5Cfrac%7B2%5Ctimes%200.15%7D%7B0.3%2B0.15%7D%5Ctimes%200%5C%5C%5CRightarrow%20v_1%3D0.27%5C%20m%2Fs)
The final velocity of the first glider is 0.27 m/s in the same direction as the first glider
![v_{2}=\frac{2m_1}{m_1+m_2}u_{1}+\frac{m_2-m_1}{m_1+m_2}u_2\\\Rightarrow v_2=\frac{2\times 0.3}{0.3+0.15}\times 0.8+\frac{0.3-0.15}{0.3+0.15}\times 0\\\Rightarrow v_2=1.067\ m/s](https://tex.z-dn.net/?f=v_%7B2%7D%3D%5Cfrac%7B2m_1%7D%7Bm_1%2Bm_2%7Du_%7B1%7D%2B%5Cfrac%7Bm_2-m_1%7D%7Bm_1%2Bm_2%7Du_2%5C%5C%5CRightarrow%20v_2%3D%5Cfrac%7B2%5Ctimes%200.3%7D%7B0.3%2B0.15%7D%5Ctimes%200.8%2B%5Cfrac%7B0.3-0.15%7D%7B0.3%2B0.15%7D%5Ctimes%200%5C%5C%5CRightarrow%20v_2%3D1.067%5C%20m%2Fs)
The final velocity of the second glider is 1.07 m/s in the same direction as the first glider.
Kinetic energy is given by
![K=\frac{1}{2}m_1v_1^2\\\Rightarrow K=\frac{1}{2}0.3\times 0.27^2\\\Rightarrow K=0.010935\ J](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7Dm_1v_1%5E2%5C%5C%5CRightarrow%20K%3D%5Cfrac%7B1%7D%7B2%7D0.3%5Ctimes%200.27%5E2%5C%5C%5CRightarrow%20K%3D0.010935%5C%20J)
Final kinetic energy of first glider is 0.010935 J
![K=\frac{1}{2}m_2v_2^2\\\Rightarrow K=\frac{1}{2}0.15\times 1.07^2\\\Rightarrow K=0.0858675\ J](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7Dm_2v_2%5E2%5C%5C%5CRightarrow%20K%3D%5Cfrac%7B1%7D%7B2%7D0.15%5Ctimes%201.07%5E2%5C%5C%5CRightarrow%20K%3D0.0858675%5C%20J)
Final kinetic energy of second glider is 0.0858675 J