Answer:
(a). The speed of the first ball after the collision is 1.95 m/s.
(b). The direction of the first ball after the collision is 44.16° due south of east.
Explanation:
Given that,
Velocity of one ball u₁= 2.2i m/s
Velocity of second ball u₂=- 0.80i m/s
Final velocity of the second ball v₂= 1.36j m/s
The mass of the identical balls are
![m = m_{1}=m_{2}](https://tex.z-dn.net/?f=m%20%3D%20m_%7B1%7D%3Dm_%7B2%7D)
(a). We need to calculate the speed of the first ball after the collision
Using law of conservation of momentum
![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)
Along X- axis
![m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}](https://tex.z-dn.net/?f=m_%7B1%7Du_%7B1%7D%2Bm_%7B2%7Du_%7B2%7D%3Dm_%7B1%7Dv_%7B1%7D)
![v_{1}=u_{1}+u_{2}](https://tex.z-dn.net/?f=v_%7B1%7D%3Du_%7B1%7D%2Bu_%7B2%7D)
Put the value into the formula
![v_{1}=2.2i-0.80i](https://tex.z-dn.net/?f=v_%7B1%7D%3D2.2i-0.80i)
![v_{1}=1.4i\ m/s](https://tex.z-dn.net/?f=v_%7B1%7D%3D1.4i%5C%20m%2Fs)
Along Y-axis
![0=m_{1}v_{1}+m_{2}v_{2}](https://tex.z-dn.net/?f=0%3Dm_%7B1%7Dv_%7B1%7D%2Bm_%7B2%7Dv_%7B2%7D)
![m_{1}v_{1}=-m_{2}v_{2}](https://tex.z-dn.net/?f=m_%7B1%7Dv_%7B1%7D%3D-m_%7B2%7Dv_%7B2%7D)
![v_{1}=-v_{2}](https://tex.z-dn.net/?f=v_%7B1%7D%3D-v_%7B2%7D)
Put the value into the formula
![v_{1}=-1.36j\ m/s](https://tex.z-dn.net/?f=v_%7B1%7D%3D-1.36j%5C%20m%2Fs)
Then the final speed of the first ball
![v_{1}=\sqrt{(1.4)^2+(1.36)^2}](https://tex.z-dn.net/?f=v_%7B1%7D%3D%5Csqrt%7B%281.4%29%5E2%2B%281.36%29%5E2%7D)
![v_{1}=1.95\ m/s](https://tex.z-dn.net/?f=v_%7B1%7D%3D1.95%5C%20m%2Fs)
(b) We need to calculate the direction of the first ball after the collision
Using formula of direction
![\tan\theta=\dfrac{v_{2}}{v_{1}}](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cdfrac%7Bv_%7B2%7D%7D%7Bv_%7B1%7D%7D)
![\tan\theta=\dfrac{-1.36}{1.4}](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cdfrac%7B-1.36%7D%7B1.4%7D)
![\theta=\tan^{-1}\dfrac{-1.36}{1.4}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Ctan%5E%7B-1%7D%5Cdfrac%7B-1.36%7D%7B1.4%7D)
![\theta=-44.16^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D-44.16%5E%7B%5Ccirc%7D)
Negative sign shows the direction of first ball .
Hence, (a). The speed of the first ball after the collision is 1.95 m/s.
(b). The direction of the first ball after the collision is 44.16° due south of east.