Momentum:

$\overline{){\mathit{p}}{\mathbf{=}}{\mathit{m}}{\mathit{v}}}$

2D vector Magnitude:

$\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathbf{v}}_{\mathbf{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{v}}_{\mathbf{y}}}^{\mathbf{2}}}}$

2D vector direction:

$\overline{){\mathbf{tan}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{v}}_{\mathit{y}}}{{\mathit{v}}_{\mathit{x}}}}$

The first car is headed south (negative y-axis). The second car is headed west (negative x-axis)

We'll use vector magnitude expression to combine the x and y components of final velocity.

**When the initial velocities are given, it is convenient to determine the final velocities in the x and y directions.**

Conservation of momentum:

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 kg and is approaching at 8.00 m/s due south. The second car has a mass of 850 kg and is approaching at 17.0 m/s due west.

A. Calculate the final velocity (magnitude and direction) of the cars.

Note that because both cars have an initial velocity, you cannot use the equations for conservation of momentum along the x-axis and y-axis; instead, you must look for other simplifying aspects.

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