(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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}

3. 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?

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# Inelastic Collision in Two Dimensions

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