Two vehicles are travelling along a straight stretch of road. The first
vehicle, mass *m*_{l} = 1200 kg, abruptly stops. The vehicle
behind, mass *m*_{2} =
1000 kg, is unable to stop in time and hits the first vehicle at a speed
of 15 m/s. After the collision the first vehicle is moving forward at *10
m/s. *Find the velocity of the second vehicle after the collision.

(b)Draw a diagram showing the two vehicles immediately *after *the
collision. (See above)

Put the *x*-axis along the direction that both vehicles are moving.

(d) Calculate the momentum of the system of two vehicles in the *before
and after *states. How many

Only one

Use an algebraic symbol for any unknown quantities.

Momentum | Before |
. | . | After |
||

component | Vehicle 1 | Vehicle 2 | Total | Vehicle 1 | Vehicle 2 | Total |

P_{x} |
0 | m_{2}v_{i} |
m_{1}v_{i} |
m_{1}v_{1} |
m_{2}v_{2} |
m_{1}v_{1}+m_{2}v_{2} |

Set totals equal

m_{2}v_{i }= m_{1}v_{1 }+ m_{2}v_{2}

Solve for the velocity of vehicle 2. **Comment **on your result.

v_{2 }= v_{i} - m_{1}v_{1 }/m_{2
}=
15 m/s- (10 m/s)(1200 kg / 1000 kg) = 15 m/s - (10 m/s)12/10
= 3 m/s

Car #2 is moving in the plus *x*- direction at 3 m/s. This seems
like a reasonable result.

If you got everything done, then estimate the force exerted on the first car by the second.

Car 1#s momentum changes by an amount *p*_{f }- *p*_{i}
= *m*_{1}(10 m/s - 15 m/s ) = -( 1200 kg)(5 m/s) = -6000 N.s.

Estimating that the collision lasts about one half second, we estimate
the force to be about:

*F = I/t = *6000
N.s / 1/2 s = 12000 N. (We used the magnitudes of the vectors here,
not the components.)

This is about 10 times the weight of the car - enough to do some damage.