Comparing Momentum and Velocity

[Minho]

Homework Statement

A car and a truck have the same kinetic energy, but the car's mass is one fifth that of the truck. Compare the velocity and momentum of the car with those of the truck.

Homework Equations

KE=1/2mv^2
p=mv

The Attempt at a Solution

I am not really sure what to do here. I tried setting up the Kinetic energy equal to each other, but then the mass and velocity would cancel each other out an I am left with 1/2=1/10. My other method was subtracting the 2 energys, but that doesn't make sense now that I am thinking about it...

Any tips on how to do this?

 

[ideasrule]

Call the truck's mass m and the truck's velocity Vt. What would its kinetic energy be? How about the car's kinetic energy? If you set those equal to each other, you'll get the right answer.

 

[Minho]

Call the truck's mass m and the truck's velocity Vt. What would its kinetic energy be? How about the car's kinetic energy? If you set those equal to each other, you'll get the right answer.

so... 1/2m(Vt^2)=1/2(1/5m)(Vc^2)
1/2m(Vt^2)=1/10m(Vc^2)
5(Vt^2)=Vc^2
Square root of 5 x Vt = VC?

 

[ideasrule]

Yes.

 

[Minho]

All right, now in solving for the potential momentum of the car compared with the truck.

using p=mv, I found the momentum of the truck to be Pt=mVt. I rewrote the equation so that Vt=m/Pt.

I then found the momentum of the car to be Pc=1/5m x (√5 x Vt) <-- velocity of the car. I substituted the Vt so that Pc= 1/5m x √5 x mVt. I canceled out the m's, so all I am left with is Pc= √5 x Vt/ 5.