Explanation:
It is given that,
Mass of the car 1, ![m_1=900\ kg](https://tex.z-dn.net/?f=m_1%3D900%5C%20kg)
Initial speed of car 1,
(east)
Mass of the car 2, ![m_2=750\ kg](https://tex.z-dn.net/?f=m_2%3D750%5C%20kg)
Initial speed of car 2,
(north)
(b) As the cars stick together. It is a case of inelastic collision. Let V is the common speed after the collision. Using the conservation of momentum as :
![m_1u_1+m_2u_2=(m_1+m_2)V](https://tex.z-dn.net/?f=m_1u_1%2Bm_2u_2%3D%28m_1%2Bm_2%29V)
![900\times 15i +750\times 20j=(900+750)V](https://tex.z-dn.net/?f=900%5Ctimes%2015i%20%2B750%5Ctimes%2020j%3D%28900%2B750%29V)
![13500i+15000j=1650V](https://tex.z-dn.net/?f=13500i%2B15000j%3D1650V)
![V=(8.18i+9.09j)\ m/s](https://tex.z-dn.net/?f=V%3D%288.18i%2B9.09j%29%5C%20m%2Fs)
The magnitude of speed,
![|V|=\sqrt{8.18^2+9.09^2}](https://tex.z-dn.net/?f=%7CV%7C%3D%5Csqrt%7B8.18%5E2%2B9.09%5E2%7D)
V = 12.22 m/s
(b) Let
is the direction the wreckage move just after the collision. It is given by :
![tan\theta=\dfrac{v_y}{v_x}](https://tex.z-dn.net/?f=tan%5Ctheta%3D%5Cdfrac%7Bv_y%7D%7Bv_x%7D)
![tan\theta=\dfrac{9.09}{8.18}](https://tex.z-dn.net/?f=tan%5Ctheta%3D%5Cdfrac%7B9.09%7D%7B8.18%7D)
![\theta=48.01^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D48.01%5E%7B%5Ccirc%7D)
Hence, this is the required solution.
Are there any option i could choose ?
Transformation of energy, because energy cannot be created or destroyed