Solving for initial velocity in an inelastic equation

[tjohn101]

Homework Statement

A 920 kg sports car collides into the rear end of a 2300 kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.6 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.37, calculates the speed of the sports car at impact. What was that speed?

Homework Equations

$$m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}_1 + m_2\vec{v}_2$$
$$m_1\vec{v}_1 + m_2\vec{v}_2 = (m_1 + m_2)\vec{v}_{f}$$

The Attempt at a Solution

I've done a dozen questions just like it but for some reason this one is stubborn. I have tried using the equations above but without any luck (I keep ending up with Vi1=0 for some reason), and I was wondering if someone could clarify whether the final velocities are equal to zero. I'm a little unsure on that part and knowing that will help tremendously.

Thank you guys!

 

[gamer_x_]

The final speed referenced is actually the speed right after impact. Since the cars skid for 2.6m after collision, the final speed is nonzero. You can easily determine this value by finding the force applied to stop the crashed cars.

 

[tjohn101]

The final speed referenced is actually the speed right after impact. Since the cars skid for 2.6m after collision, the final speed is nonzero. You can easily determine this value by finding the force applied to stop the crashed cars.

I'm still having trouble... Every time I try to solve for Vf I come up with 1.

 

[gamer_x_]

how did you calculate vf?

 

[tjohn101]

I've been using the momentum equation up top and the inelastic equation. I know there is another one but I can't remember it for anything.. :/

I've just been isolating Vf on one side. But every time I do the answer on both sides is always equal..

 

[gamer_x_]

You don't know the initial velocity of the speeding car to use the momentum equation. You need to determine final velocity (immediately after impact) from the friction force applied to stop the crashed car and the distance that took.

 

[tjohn101]

You don't know the initial velocity of the speeding car to use the momentum equation. You need to determine final velocity (immediately after impact) from the friction force applied to stop the crashed car and the distance that took.

I know that much, but I'm unsure of how to do it

 

[gamer_x_]

Find acceleration due to friction from Vf -> 0 after crash (F=ma). Then use kinematics formulas to get Vf from that.

 

[tjohn101]

Find acceleration due to friction from Vf -> 0 after crash (F=ma). Then use kinematics formulas to get Vf from that.

And how do I do that? I have no idea about how to solve any of this

 

[gamer_x_]

kinetic friction = only force applied = coefficient * force_normal = m*a. You also know that the change in velocity is related to acceleration through several of the kinetic equations, and they don't necessarily need time.

 

[tjohn101]

The acceleration wouldn't be 3.626 m/s^2 by any chance, would it?