Physics Kinetic energy problem

[joonkimdds]

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One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 9.0m/s, they have the same kinetic energy. what were the original speeds of the two cars?

could someone solve this one or set up this one for me?
i got -9m/s but it's wrong 🙁

 

[Nikki2002]

🙂

 

[seadizzle]

Let 2m be the mass of car 1 and m be the mass of car 2.
Let v1 be the velocit of car 1 and v2 be the velocity of car 2.

Let KE = (1/2) 2m * v1^2 be the kinetic energy of car 1

We are given the KE of car 2 is twice that of car 1, so KE of car2 is = 2m*v1^2

Notice we can obtain information from this by going back to the KE since we know for car two KE = (1/2)m*v2^2

Setting this equal we see (1/2)m*v2^2 = 2m*v1^2
Note m cancels and multiply both sides by 2:
Equation 1: v2^2 = 4*v1^2

We are also given that when the speeds are each increased by 9m/s their KEs are the same, thus we set the equality

(1/2)*2m*(v1+9)^2 = (1/2)*m*(v2+9)^2

here again the (1/2)m cancel and we get

Equation 2: 2*(v1+9)^2 = (v2+9)^2

Solve the system of equations for Equation 1 and 2
Two variables, two equations

disclaimer: i just typed this stream of thought without checking for typos
this is the idea though

 

[joonkimdds]

Let 2m be the mass of car 1 and m be the mass of car 2.
Let v1 be the velocit of car 1 and v2 be the velocity of car 2.

Let KE = (1/2) 2m * v1^2 be the kinetic energy of car 1

We are given the KE of car 2 is twice that of car 1, so KE of car2 is = 2m*v1^2

Notice we can obtain information from this by going back to the KE since we know for car two KE = (1/2)m*v2^2

Setting this equal we see (1/2)m*v2^2 = 2m*v1^2
Note m cancels and multiply both sides by 2:
Equation 1: v2^2 = 4*v1^2

We are also given that when the speeds are each increased by 9m/s their KEs are the same, thus we set the equality

(1/2)*2m*(v1+9)^2 = (1/2)*m*(v2+9)^2

here again the (1/2)m cancel and we get

Equation 2: 2*(v1+9)^2 = (v2+9)^2

Solve the system of equations for Equation 1 and 2
Two variables, two equations

disclaimer: i just typed this stream of thought without checking for typos
this is the idea though

Thank You~!