Answer:
a.
, ![29.4^{0}](https://tex.z-dn.net/?f=29.4%5E%7B0%7D)
b. ![K.E =-697.8J](https://tex.z-dn.net/?f=K.E%20%3D-697.8J)
Explanation:
To calculate the values in the question, a deep understanding of perfect inelastic collision is important.
When two bodies undergo inelastic collision, two important parameters must be well understood i.e
Momentum: the momentum is always conserved in perfectly inelastic collision. i.e the total momentum after collision is the sum of the individual momentum before collision
Kinetic energy: Kinetic energy is not conserved due to dissipative force.
a.To calculate the velocity, we first find the total momentum before collision
Momentum of player 1 ![p_{1} =mv=95kg*5m/s\\p_{1} =475kgm/s\\](https://tex.z-dn.net/?f=p_%7B1%7D%20%3Dmv%3D95kg%2A5m%2Fs%5C%5Cp_%7B1%7D%20%3D475kgm%2Fs%5C%5C)
Momentum of player 2 ![p_{2} =mv=90kg*3m/s\\p_{1} =270kgm/s\\](https://tex.z-dn.net/?f=p_%7B2%7D%20%3Dmv%3D90kg%2A3m%2Fs%5C%5Cp_%7B1%7D%20%3D270kgm%2Fs%5C%5C)
Hence the total momentum ![p_{12}=p_{1}+p_{2}\\](https://tex.z-dn.net/?f=p_%7B12%7D%3Dp_%7B1%7D%2Bp_%7B2%7D%5C%5C)
Note, since the direction of movement before collision is due south and due north respectively we have to represent the velocity using the rectangular coordinate
Hence ![p_{12}=(m_{1}+m_{2})v=p_{1}i+p_{2}j\\](https://tex.z-dn.net/?f=p_%7B12%7D%3D%28m_%7B1%7D%2Bm_%7B2%7D%29v%3Dp_%7B1%7Di%2Bp_%7B2%7Dj%5C%5C)
![(95+90)v=475i+270j\\](https://tex.z-dn.net/?f=%2895%2B90%29v%3D475i%2B270j%5C%5C)
![v=2.57i+1.45j\\](https://tex.z-dn.net/?f=v%3D2.57i%2B1.45j%5C%5C)
solving for the resultant velocity, we have
To calculate the direction of movement, we have
![\alpha =tan^{-1}=\frac{v_{j} }{v_{i}}\\ \alpha =tan^{-1}=\frac{1.45}{2.57}\\\alpha =29.4^{0}](https://tex.z-dn.net/?f=%5Calpha%20%3Dtan%5E%7B-1%7D%3D%5Cfrac%7Bv_%7Bj%7D%20%7D%7Bv_%7Bi%7D%7D%5C%5C%20%20%5Calpha%20%3Dtan%5E%7B-1%7D%3D%5Cfrac%7B1.45%7D%7B2.57%7D%5C%5C%5Calpha%20%3D29.4%5E%7B0%7D)
b. to calculate the decrease in total kinetic energy, before collision, the total kinetic was
![K.E_{initial} =\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}.\\K.E_{initial} =((1/2)*95*5^{2})+((1/2)*90*3^{2})\\K.E_{initial} =1187.5+405\\K.E_{initial} =1592.5J\\](https://tex.z-dn.net/?f=K.E_%7Binitial%7D%20%3D%5Cfrac%7B1%7D%7B2%7Dm_%7B1%7Dv_%7B1%7D%5E%7B2%7D%2B%5Cfrac%7B1%7D%7B2%7Dm_%7B2%7Dv_%7B2%7D%5E%7B2%7D.%5C%5CK.E_%7Binitial%7D%20%3D%28%281%2F2%29%2A95%2A5%5E%7B2%7D%29%2B%28%281%2F2%29%2A90%2A3%5E%7B2%7D%29%5C%5CK.E_%7Binitial%7D%20%3D1187.5%2B405%5C%5CK.E_%7Binitial%7D%20%3D1592.5J%5C%5C)
And the final kinetic energy after collision is
![K.E_{final} =\frac{1}{2}(m_{1}+m_{2} )v^{2}\\ K.E_{final} =\frac{1}{2}(95+90)* 3.11^{2}\\ K.E_{final} =894.7J](https://tex.z-dn.net/?f=K.E_%7Bfinal%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%28m_%7B1%7D%2Bm_%7B2%7D%20%29v%5E%7B2%7D%5C%5C%20%20K.E_%7Bfinal%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%2895%2B90%29%2A%203.11%5E%7B2%7D%5C%5C%20K.E_%7Bfinal%7D%20%3D894.7J)
The decrease in Kinetic energy is
![K.E =K.E_{final}- K.E_{initial}=894.7-1592.5](https://tex.z-dn.net/?f=K.E%20%3DK.E_%7Bfinal%7D-%20K.E_%7Binitial%7D%3D894.7-1592.5)
![K.E =-697.8J](https://tex.z-dn.net/?f=K.E%20%3D-697.8J)
The negative sign indicate a decrease in Kinetic energy