## anonymous one year ago Two hard steel balls collide in a perfectly elastic collision. The first ball has a mass of 1kg and is traveling at 5m/s east. The second ball has a mass of 2kg and is initially traveling at 7 m/s west along the same path so they collide head on. After the collision the second ball is traveling at 1m/s east. What is the velocity of the 1st ball after the collision? **How do I solve and show the work for this? :/ Thanks!!

1. Michele_Laino

here we have to apply the law of conservation of total momentum and the law of conservation of kinetic energy, since the collision is elastic

2. Michele_Laino

the situation, before collision is: |dw:1433610623171:dw|

3. anonymous

ok!

4. Michele_Laino

so, total momentum is: $\Large {m_1}{v_1} - {m_2}{v_2} = 1 \times 5 - 2 \times 7 = ...$

5. anonymous

ok! so we get 5-14? = -9 ?

6. Michele_Laino

minus sign, means that the vector of the resultant momentum is oriented towards west

7. anonymous

ohh okay! so -9, meaning 9 m/s to the west is the velocity of the 1st ball after collision?

8. Michele_Laino

no, -9 is the magnitude and sign of the resultant momentum

9. anonymous

ohh okay! so it's like this? 5-14=-9 =resultant momentum ?

10. Michele_Laino

yes! now total kinetic energy is: $\large KE = \frac{1}{2}{m_1}v_1^2 + \frac{1}{2}{m_2}v_2^2 = \frac{1}{2} \times 1 \times 25 + \frac{1}{2} \times 2 \times 49 = ...$

11. anonymous

ok! so we get this? 61.5 ?

12. Michele_Laino

ok! correct!

13. Michele_Laino

now let's consider the situation after the collision

14. anonymous

ohhh so 61.5 is just the KE right? so we solve for velocity now? :/

15. Michele_Laino

|dw:1433611229406:dw|

16. Michele_Laino

no, we have to apply the conservation of total momentum first

17. anonymous

oh ok! how do we do that?

18. Michele_Laino

I call with u the speed of the first ball after collision

19. anonymous

ok!

20. Michele_Laino

so we can write: conservation of total momentum: $\Large \begin{gathered} {m_1}u + {m_2}v{'_2} = - 9 \hfill \\ 1 \times u + 7 \times 1 = - 9 \hfill \\ \end{gathered}$

21. Michele_Laino

what is u?

22. anonymous

-16?

23. Michele_Laino

in my reasoning i have considered positive velocity if the velocity is towards east, and negative velocity if that velocity is towards west

24. anonymous

oh! so u=-16?

25. anonymous

16 m/s to the west?

26. Michele_Laino

correct! that means the first ball, after the collision is goinf towards west

27. Michele_Laino

going*

28. anonymous

ahh so that is our solution? :O

29. Michele_Laino

yes!

30. anonymous

yay!! thank you!:D

31. Michele_Laino

:)