The concept that we need to give solution to this problem is collision equation given by momentum conservation,
Our values are,
[tex]m_2 = 0.145 kg\\u_2 = 34.5 m/s\\m_1 = 34 kg\\u_1 = 0[/tex]
Then,
Part A) We can here note that the velocity for the puck is zero (there is not a velocity in that direction)
[tex] V_{goalie} = \frac{m_1-m_2}{m_1+m_2}V_{01} + \frac{2m_2}{m_1+m_2}V_{02}[/tex]
[tex]V_{goalie} = \frac{34-0.145}{34+0.145}(0)+\frac{2*0.145}{34+0.145}(34.5)[/tex]
[tex]V_{goalie} = 0.2930m/s[/tex]
Part B ) We apply the same solution but know we note that in the collision for the Goalie the velocity is zero.
[tex]V_{puck} = \frac{m_1-m_2}{m_1+m_2}V_{02} + \frac{2m_2}{m_1+m_2}V_{01}[/tex]
[tex]V_{puck} = \frac{34-0.145}{34+0.145}(34.5)+\frac{2*0.145}{34+0.145}(0)[/tex]
[tex]V_{puck} = 34.20m/s[/tex]