56. We denote the velocity of the player with

v

1

and the relative velocity between the player and the ball be

v

2

. Then the velocity

v of the ball relative to the field is given by

v =

v

1

+

v

2

. The smallest angle θ

min

corresponds to the case when

v

⊥
v

1

. Hence,

θ

min

=

18 0

◦

− cos

−1

|
v

1

|

|
v

2

|



=

18 0

◦

− cos

−1

4.0 m/s

6.0 m/s



≈ 130

◦

.

goal

θ

min

-

v

1

6

v

H

H

H

H

H

H

Y

v

2