As per Impulse momentum theorem we know that
Impulse = final momentum - initial momentum
so now here we have
impulse = 27.95 N-s
mass = 59.11 kg
final speed = 6.129 m/s
now we have
[tex]I = m(v_f - v_i)[/tex]
[tex]27.95 = 59.11(6.129 - v_i)[/tex]
[tex]0.473 = 6.129 - v_i[/tex]
[tex]v_i = 6.129 - 0.473[/tex]
[tex]v_i = 5.656 m/s[/tex]
so initial speed must be 5.656 m/s