Calculating Time Interval for a Perfectly Elastic Collision in Curling Match

[ElementUser]

Homework Statement

Matthew and Amanda have challenged Trevor and Julie to a curling match, played with perfectly elastic rocks sliding on level frictionless ice. Three rocks are lined up all in a row (perfectly straight line). B is a junior rock and its mass is exactly half of A or C. B and C are stationary while A approaches. Calculate the time interval between the collision of A&B and the collision of B&C. The distance between B and C is 4.5m. Rock A has an initial velocity of 1.5 m/s.

Diagram: 2M -----> M __________ 2M
Distance between M and the right-most 2M is 4.5m.

Homework Equations

m1v1+m2v2=m1v1^prime + m2v2^prime
d=vt, where v is equal to v2^prime
J=Ft
p=mv
Probably some equation that I missed (main problem of the question that I can't figure out)

The Attempt at a Solution

Variables: m1=2 kg
m2=1 kg
v1=1.5 m/s
v2=0 m/s
v1^prime=?
v2^prime=?

2(1.5)+0=2v1^prime+v2^prime
3=2v1^prime+v2^prime

Then I tried doing v2^prime=d/t, which got me to:

v2^prime=4.5/t

I tried subbing that into the other equation to make it 3=2v1^prime+v2^prime, but that got me nowhere. So basically I'm stuck trying to find v2^prime, which is what I need to figure out the time interval between the 2 collisions. I tried to think of the impulse&momentum equations, but they didn't seem to help (can't find the force for the impulse equation).

Any help is appreciated! Thanks :).

-ElementUser (first post in these forums)

 

[tiny-tim]

Welcome to PF!

… a curling match, played with perfectly elastic rocks sliding on level frictionless ice …

Hi ElementUser! Welcome to PF!

(no need to write ^prime … just write ' )

In exam questions, "perfectly elastic" means you can use conservation of energy.

 

[ElementUser]

Thanks tiny-tim :)

Took me a long time because my physics teacher today added a portion for this question, that you also have to find the time interval for the second timer Rock B will hit Rock A (after B bounces off of C).