anonymous
  • anonymous
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 ?
Physics
katieb
  • katieb
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Michele_Laino
  • Michele_Laino
here we have to apply the total momentum conservation law
Michele_Laino
  • Michele_Laino
|dw:1433014089573:dw|
anonymous
  • anonymous
ok:)

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Michele_Laino
  • Michele_Laino
we have to find the momentum p_1 and the momentum p_2
Michele_Laino
  • Michele_Laino
so we have: \[\begin{gathered} {p_1} = 1600 \times 10 = ... \hfill \\ \hfill \\ {p_2} = 1400 \times 15 = ... \hfill \\ \end{gathered} \]
anonymous
  • anonymous
okay so we get 16000 and 21000?
Michele_Laino
  • Michele_Laino
correct!
anonymous
  • anonymous
yay!! what happens now?
Michele_Laino
  • 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: \[\Large \begin{gathered} {P_1} = \left( {{m_1} + {m_2}} \right){V_1} = {p_1} \hfill \\ \hfill \\ P2 = \left( {{m_1} + {m_2}} \right){V_2} = {p_2} \hfill \\ \end{gathered} \]
Michele_Laino
  • 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|
anonymous
  • anonymous
yes :) how do we find the speed from that?
Michele_Laino
  • Michele_Laino
we have to divide the formulas above, by m_1+m_2, like this: \[\Large \begin{gathered} {V_1} = \frac{{{p_1}}}{{{m_1} + {m_2}}} \hfill \\ \hfill \\ {V_2} = \frac{{{p_2}}}{{{m_1} + {m_2}}} \hfill \\ \end{gathered} \]
anonymous
  • anonymous
ok! what do we plug in? :/
Michele_Laino
  • Michele_Laino
it is simple: p_1=10,000, p_2=21,000, m_1=1,600 and m_2=1,400
anonymous
  • anonymous
ok! so we get 7?
Michele_Laino
  • Michele_Laino
and the othe velocity?
Michele_Laino
  • Michele_Laino
other*
anonymous
  • anonymous
it is 3.333 (oops sorry forgot to write this one earlier haha)
Michele_Laino
  • Michele_Laino
I got 5.33
anonymous
  • anonymous
ohh yes sorry!! so from there what do we do?
Michele_Laino
  • Michele_Laino
ok! so the requested velocity, has the subsequent magnitude: \[V = \sqrt {V_1^2 + V_2^2} = \sqrt {{{5.33}^2} + {7^2}} = ...\]
anonymous
  • anonymous
8.79? so our solution is 8.8 m/s?
Michele_Laino
  • Michele_Laino
yes! That's right!
anonymous
  • anonymous
yay!! thank you!!
Michele_Laino
  • Michele_Laino
:):)

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