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## Homework Statement

A 1300-kg car collides with a 15,000-kg truck at an intersection and they couple together and move off as one leaving a skid mark 5m long that makes an angle of 30.0° with the original direction of the car. If μ

_{k}= 0.700, find the initial velocities of the car and truck before the collision.

Note: The car is travelling east and the truck is travelling north.

## Homework Equations

F

_{IMPACT}=F

_{FRICTION}

F = μ * m * g

F = m * a

v

^{2}=v

_{0}

^{2}+ 2 * a * x

x component of momentum: (m

_{1}+ m

_{2}) * V

_{f}* cos θ = m

_{1}* v

_{1i}

y component of momentum: (m

_{1}+ m

_{2}) * V

_{f}* cos θ = m

_{2}* v

_{2i}

## The Attempt at a Solution

The force at impact equals the force of friction: F = (0.700)(16300 kg)(9.8 m/s^2) = 111818 N

Find deceleration of the system: a = 111818 N / 16300 kg = 6.86 m/s^2

Use kinematic equation to find v

_{0}: 0 = v

_{0}

^{2}+ (2)(6.86 m/s^2)(5 m); v

_{0}= 8.28 m/s

x component: (16300 kg)(8.28 m/s^2)(cos 30°) = 1300 * v

_{1i}; v

_{1i}= 89.7 m/s

y component: (16300 kg)(8.28 m/s^2)(sin 30°) = 15000 * v

_{2i}; v

_{2i}= 4.49 m/s

Obviously the initial velocity for the car is outlandish at 89.7 m/s. I've tried a couple of other equations and I keep getting this same answer. I think the problem is that I am assuming that V

_{f}= v

_{0}. When I use tan θ = (m

_{2}* v

_{2i}) / (m

_{1}* v

_{1i}) I get v

_{2i}/ v

_{1i}= 0.05. If the speed of the car gets much lower the truck will hardly be moving so I am baffled.

Should I try calculating V

_{f}by figuring out the kinetic energy instead?