How Do You Calculate Original Speeds from Mass and Kinetic Energy Differences?

[don123]

One car has two and a half times the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 7.0 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?


let x = mass of second car
thus mass of first car = 2.5x
let a = speed of first car
let b = speed of Second car

0.5 * 2.5x * (a+7)^2 = 0.5 * x * (b+7)^2 (equation 1)

2 * 0.5 * 2.5x * a^2 = 0.5 * x * b^2
2.5x * a^2 = 0.5 * x * b^2 (equation)

0.5 * 2.5x * (a+7)^2 = 0.5 * x * (b+7)^2 (equation 1)

2 * 0.5 * 2.5x * a^2 = 0.5 * x * b^2
2.5x * a^2 = 0.5 * x * b^2 (equation 2)

Herre are the equations I got, but didn't get the right answers still. Help anyone?

 

[Doc Al]

Your equations look OK. (They can be further simplified, of course: things can be canceled and rearranged.) Since you didn't provide your solution of the equations, I can't tell where you went wrong.

 

[don123]

I got a = 5.17 and b = 9.02 for my starting velocities.

 

[Doc Al]

Describe how you solved those equations. I suggest simplifying those two equations as much as possible, then resolving them step by step.