75. We choose ˆi East and ˆj North, and use SI units. The ball initially moving eastward has mass m

1

= 5.0 kg

and initial velocity 

v

1i

= 4.0ˆi m/s, and the ball initially moving westward has mass m

2

= 4.0 kg and

velocity 

v

2i

=

−3.0ˆi m/s. The final velocity of m

1

is 

v

1f

=

−1.2ˆj.

(a) Momentum conservation leads to

m

1



v

1i

+ m

2



v

2i

=

m

1



v

1

+ m

2



v

2

20ˆi

− 12ˆi = −6ˆj + 4v

2

which leads to



v

2

= 2.0ˆi + 1.5ˆj =

⇒ v

2

=(2.5

37

◦

)

where magnitude-angle notation is used. Thus, the speed of the 4.0 kg ball just after the collision
is 2.5 m/s.

(b) We compute the decrease in total kinetic energy:

K

i

− K

f

=

1

2

(5)(4)

2

+

1

2

(4)(3)

2

−

1

2

(5)(1.2)

2

−

1

2

(4)(2.5)

2

which gives the result 42 J.