# Homework Help: Speed ratio

1. Nov 2, 2008

### bmandrade

Particle A has three times the mass and twice the kinetic energy of particle B. what is the speed ratio Va/Vb

2. Nov 2, 2008

### hage567

You need to show some work before you can receive help. What have you tried so far?

3. Nov 2, 2008

### bmandrade

Well i am working on it and I came up with equations

2k= 1/2*3M*Va
k=1/2*M* Vb

but I got stuck I really dont know what to do with this equations

4. Nov 2, 2008

### hage567

Your equation for kinetic energy is wrong. The velocity is supposed to be squared.

So you have two equations. How do you think you might put them together?

5. Nov 2, 2008

### bmandrade

equal to each other i was thiking maybe dividing the firt equation by 2 so that both equations equal to K

6. Nov 2, 2008

### hage567

OK. Then what?

7. Nov 2, 2008

### bmandrade

equal each other and solve for Va/Vb?

8. Nov 2, 2008

### bmandrade

it gives me 1/6

9. Nov 2, 2008

### bmandrade

sorry 1/36

10. Nov 2, 2008

### hage567

Can you show more of the steps on how you got that number?

11. Nov 2, 2008

### bmandrade

ok so i did it again and i notices i had skipped a step and got a new answer which is square root of 1/3

here is the work

2k= 1/2 3M Va^2 divide by 2
k= (3M Va^2) / 2 set it equal to the other equation
(3M Va^2)/ 2 = 1/2 M Vb^2 muiltiply by 2
3M Va^2 = M Vb^2 divide by Vb^2
3M Va^2/Vb^2 = M divide by 3M
Va^2/ Vb^2 = M/3M M's cancel and take square root
Va/Vb = square root of 1/3!~

12. Nov 2, 2008

### hage567

You are almost right, you are missing a factor of 2 somewhere.

You had

2k= 1/2*3M*Va^2
k=1/2*M* Vb^2

so if you divide the first equation by 2, like you said you were going to do in post #5, you get

k = 1/4*3M*Va^2

right? I think you forgot about the 1/2 on the right side. Do you see that?

So now if you set the two equations equal to each other and solve, what do you get?

13. Nov 2, 2008

### bmandrade

right!!! i was saw that error
in that case the ratio is square root of 2/3!

14. Nov 2, 2008

### hage567

That looks much better!

15. Nov 2, 2008

### bmandrade

thank you !!!!

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