Answer:
The final velocity of the cars is 6.894 m/s
The kinetic energy lost is 117,441 J
Step-by-step explanation:
Using the conservation of the linear momentum :

Where
is the inicial linear momentum and
is the final linear momemtum.
The linear momentum is calculated by:

where M is the mass and V is the velocity.
First we identify the directions of the velocity of both cars:
- the first car is moving in the axis y for the south direction, we will take this direction like positive.
- the second car is moving in the axis x to the west, we will take this direction like positive.
The conservation of the linear momentum is made on direction x, so:

where
is the mass of the car 1,
is the car 1's inicial velocity in the axis x,
is the mass of the car 2,
is the car 2's inicial velocity in the axis x and
is the velocity of the car 1 and car 2 after the collition.
The car 1 just move in the axis y so, it dont have horizontal velocity (
= 0)
now the equation is:

Replacing the values, we get:
(700 kg)(21 m/s) =
( 1800 kg + 700 kg)
solving for
:

= 5.88 m/s
Now we do the conservation of the linear momentum on direction y:

where
is the mass of the car 1,
is the car 1's inicial velocity in the axis y,
is the mass of the car 2,
is the car 2's inicial velocity in the axis y and
is the velocity of the car 1 and car 2 together after the collition.
The car 2 just move in the axis x so, it don't have horizontal velocity (
= 0)
now the equation is:

Replacing the values, we get:

solving for
:

= 3.6 m/s
Now, we have the two components of the velocity and using pythagorean theorem we find the answer as:

6.894 m/s
Finally we have to find the kinetic energy lost, so the kinetic energy is calculated by:
K =

so, ΔK =

where
is the final kinetic energy and
is the inicial kinetic energy.
then:


so:
ΔK = 59409 - 176850 = -117441 J