Question

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 ?

Answer 1

here we have to apply the total momentum conservation law

Answer 2

ok:)

Answer 3

we have to find the momentum p_1 and the momentum p_2

Answer 4

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

Answer 5

okay so we get 16000 and 21000?

Answer 6

correct!

Answer 7

yay!! what happens now?

Answer 8

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:
\[\Large \begin{gathered}
{P_1} = \left( {{m_1} + {m_2}} \right){V_1} = {p_1} \hfill \\
\hfill \\
P2 = \left( {{m_1} + {m_2}} \right){V_2} = {p_2} \hfill \\
\end{gathered} \]

Answer 9

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:

Answer 10

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

Answer 11

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

Answer 12

ok! what do we plug in? :/

Answer 13

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

Answer 14

ok! so we get 7?

Answer 15

and the othe velocity?

Answer 16

other*

Answer 17

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

Answer 18

I got 5.33

Answer 19

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

Answer 20

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

Answer 21

8.79? so our solution is 8.8 m/s?

Answer 22

yes! That's right!

Answer 23

yay!! thank you!!

Answer 24

:):)