## anonymous one year ago A 1,600 kg car traveling north at 10.0 m/s crashes into a 1,400 kg car traveling east at 15 m/s at an unexpectedly icy intersection. The cars lock together as they skid on the ice. What is their speed after the crash? 8.8 m/s , 12 m/s , 18 m/s , or 26 m/s ?

1. Michele_Laino

here we have to apply the total momentum conservation law

2. Michele_Laino

|dw:1433014089573:dw|

3. anonymous

ok:)

4. Michele_Laino

we have to find the momentum p_1 and the momentum p_2

5. Michele_Laino

so we have: $\begin{gathered} {p_1} = 1600 \times 10 = ... \hfill \\ \hfill \\ {p_2} = 1400 \times 15 = ... \hfill \\ \end{gathered}$

6. anonymous

okay so we get 16000 and 21000?

7. Michele_Laino

correct!

8. anonymous

yay!! what happens now?

9. Michele_Laino

now, after collision, the system car #1 + car#2 has two components of its momentum, namely P_1 and P_2 such that the subsequent condition holds: $\Large \begin{gathered} {P_1} = \left( {{m_1} + {m_2}} \right){V_1} = {p_1} \hfill \\ \hfill \\ P2 = \left( {{m_1} + {m_2}} \right){V_2} = {p_2} \hfill \\ \end{gathered}$

10. Michele_Laino

where m_1 and m_2 are the masses of the two cars respectively, and V_1 and V_2 are the components of the velocity of the system car #1 + car#2, namely: |dw:1433014582296:dw|

11. anonymous

yes :) how do we find the speed from that?

12. Michele_Laino

we have to divide the formulas above, by m_1+m_2, like this: $\Large \begin{gathered} {V_1} = \frac{{{p_1}}}{{{m_1} + {m_2}}} \hfill \\ \hfill \\ {V_2} = \frac{{{p_2}}}{{{m_1} + {m_2}}} \hfill \\ \end{gathered}$

13. anonymous

ok! what do we plug in? :/

14. Michele_Laino

it is simple: p_1=10,000, p_2=21,000, m_1=1,600 and m_2=1,400

15. anonymous

ok! so we get 7?

16. Michele_Laino

and the othe velocity?

17. Michele_Laino

other*

18. anonymous

it is 3.333 (oops sorry forgot to write this one earlier haha)

19. Michele_Laino

I got 5.33

20. anonymous

ohh yes sorry!! so from there what do we do?

21. Michele_Laino

ok! so the requested velocity, has the subsequent magnitude: $V = \sqrt {V_1^2 + V_2^2} = \sqrt {{{5.33}^2} + {7^2}} = ...$

22. anonymous

8.79? so our solution is 8.8 m/s?

23. Michele_Laino

yes! That's right!

24. anonymous

yay!! thank you!!

25. Michele_Laino

:):)