Kinetic Energy/Velocity Relationship

[bmyer]

Homework Statement

One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 5.7 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?

Homework Equations

KE=1/2mv^2, where KE equals kinetic energy.

The Attempt at a Solution

Don't know where to start.
Car 1: .5KE=(1/2)(m)(v1^2)
Car 2: KE = (1/2)(.5m)(v2^2)

You can set the 2 equations equal in KE when 5.7 is added to both v1 and v2, but there are still too many variables! I have been stuck on this problem for 2 hours and I am about to go crazy! Please help!

 

[rl.bhat]

Car 1: .5KE=(1/2)(m)(v1^2)
Car 2: KE = (1/2)(.5m)(v2^2)
Take the ratio of the above two equations. You get the relation between V1 and V2.
You can set the 2 equations equal in KE when 5.7 is added to both v1 and v2
Use the above relation to solve the next two equations.