Friction force,

$\overline{){{\mathit{f}}}_{{\mathbf{k}}}{\mathbf{=}}{{\mathit{\mu}}}_{{\mathbf{k}}}{\mathit{m}}{\mathit{g}}}$

Work done,

$\overline{){\mathit{W}}{\mathbf{=}}{{\mathit{f}}}_{{\mathbf{k}}}{\mathit{d}}}$

Kinetic energy,

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

Conservation of momentum,

$\overline{)\begin{array}{rcl}{\mathbf{m}}_{\mathbf{t}}{\mathbf{v}}_{\mathbf{0}\mathbf{t}}\mathbf{+}{\mathbf{m}}_{\mathbf{c}}{\mathbf{v}}_{\mathbf{0}\mathbf{c}}& \mathbf{=}& \mathbf{(}{\mathbf{m}}_{\mathbf{t}}\mathbf{+}{\mathbf{m}}_{\mathbf{c}}\mathbf{)}{\mathbf{v}}_{\mathbf{f}}\end{array}}$

Vector magnitude,

$\overline{)\begin{array}{rcl}\mathbf{\left|}\mathbf{v}\mathbf{\right|}& {\mathbf{=}}& \sqrt{{\mathbf{\left(}{\mathbf{v}}_{\mathbf{x}}\mathbf{\right)}}^{\mathbf{2}}\mathbf{+}{\mathbf{\left(}{\mathbf{v}}_{\mathbf{y}}\mathbf{\right)}}^{\mathbf{2}}}\end{array}}$

m_{c} = 1000 kg

v_{c }= - 5.0 m/s î

m_{t }= 1500 kg

v_{t} = - 6.0 m/s ju

μ_{k} = 0.5.

A car with mass m_{c} = 1000 kg is traveling west through an intersection at a magnitude of velocity of v_{c }= 5.0 m/s when a truck of mass m_{t} = 1500 kg traveling south at v_{t} = 6.0 m/s fails to yield and collides with the car. The vehicles become stuck together and slide on the asphalt, which has a coefficient of friction with the rubber tires of μ_{k} = 0.5.

How far, in meters, will the vehicles slide after the collision?

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