What is the speed of recoil of the chair and cat?

[Sneakatone]

Homework Statement

A cat crouches on the floor at a distance of 1.7 m from a desk chair of height 0.45 m. The cat jumps onto the chair , landing with zero vertical velocity. The desk chair has coasters and rolls soomthly away when the cat lands. The cats mass is 6.4 kg , the chairs mass is 12 kg. what is the speed of recoil of the chair and cat?

The Attempt at a Solution

1/2gt^2=0.45m
t=0.303s
1.7/0.303=5.61ms horizontal velocity component
5.61*6.4=12v
v=2.99m/s

 

[Doc Al]

1/2gt^2=0.45m
t=0.303s
1.7/0.303=5.61ms horizontal velocity component

So far, so good.

5.61*6.4=12v

After the "collision" the chair and cat move as one body.

 

[Sneakatone]

so would it be 5.61*6.4=(12+6.4)v?

 

[Doc Al]

so would it be 5.61*6.4=(12+6.4)v?

That's correct.

 

[Sneakatone]

thank you!
was that center of mass equation used or was that m1v11=m2v1?

 

[Doc Al]

thank you!
was that center of mass equation used or was that m1v11=m2v1?

That was conservation of momentum applied to an inelastic collision.

m1v1 + m2v2 = (m1 + m2)vf

(Here, v2 = 0, since the chair was initially at rest.)

 

[Sneakatone]

I see now,
thank you very much!