Inelastic Collision of 2 Carts - Displacement

[testme]

Homework Statement

A 15.0 kg toy cart is traveling at 5.5 m/s to the right when it collides head on with a 10.0 kg cart traveling at 4.0 m/s to the left. The objects collide and stick togethere. The coefficient of friction between the wheels of the cart and the floor is 0.40. How far will the carts slide from the location of the collision?

ma = 15 kg
va = 5.5 m/s
mb = 10 kg
vb = 4.0 m/s
μ = 0.4

Homework Equations

Assuming right is positive.

mava + mbvb = ma+b * va+b
Fnet = ma
v2^2 = v1^2 + 2ad

The Attempt at a Solution

mava + mbvb = ma+b * va+b
15(5.5) + 10(-4) = 25 * va+b
42.5 = 25 * va+b
va+b = 1.7 m/s

Fnet = ma
Ff = ma
Fnμ = ma
- Since there is no vertical acceleration Fn = Fg
9.8(0.4) = a
a = -3.92 m/s

this is where I get stuck

Edit: I tried doing this but I'm not sure if I'm right.

v2^2 = v1^2 + 2ad
0 = (1.7)^2 + 2(-3.92)d
-2.89 = -7.84d
d = 0.37 m

 

[gneill]

Yup. That works