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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Collisions & Motion (Momentum & Energy) concept. You can view video lessons to learn Collisions & Motion (Momentum & Energy). Or if you need more Collisions & Motion (Momentum & Energy) practice, you can also practice Collisions & Motion (Momentum & Energy) practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Mochrie's class at YU.