Originally Posted by **Raj** A car at rest, Mass 1850kg, is hit from behind by a truck, travelling at 65.1km/h. After impact they lock together and travel at 26.2km/h. What is the mass of the truck?
I came up with this equation:
m1v1 + m2v2 = (m1+m2)v3
65.1m = 26.2m1 + 26.2m2
Stuck and need help =\ |

You've got the right idea, but I'm not clear on your notation.

So let's define $\displaystyle m_1$ to be the mass of the car at rest, $\displaystyle m_2$ the mass of the truck, $\displaystyle v_{10}$ the speed of the car before the collision, $\displaystyle v_{20}$ the speed of the truck before the collision, and v the speed of the combined mass after the collision. Then by conservation of momentum:

$\displaystyle m_1v_{10} + m_2v_{20} = (m_1 + m_2)v$

Plugging in what we know gives us

$\displaystyle 1850(0) + m_2(61.5) = (1850 + m_2)(26.2)$

$\displaystyle m_2(61.5) = (1850 + m_2)(26.2)$

Now solve for $\displaystyle m_2$.

Note that this is not an elastic collision since the two masses are stuck together after the collision, so we can't use conservation of energy here.

-Dan