41.

(a) Let m

1

be the mass of the body that is originally moving, v

1i

be its velocity before the collision,

and v

1f

be its velocity after the collision. Let m

2

be the mass of the body that is originally at rest

and v

2f

be its velocity after the collision. Then, according to Eq. 10–30,

v

1f

=

m

1

− m

2

m

1

+ m

2

v

1i

.

We solve for m

2

to obtain

m

2

=

v

1i

− v

1f

v

1f

+ v

1i

m

1

.

We combine this with v

1f

= v

1i

/4 to obtain m

2

= 3m

1

/5 = 3(2.0)/5 = 1.2 kg.

(b) The speed of the center of mass is

v

com

=

m

1

v

1i

+ m

2

v

2i

m

1

+ m

2

=

(2.0)(4.0)

2.0 + 1.2

= 2.5 m/s .