Well, to calculate the goalie's speed after catching the puck, we can use the law of conservation of momentum. The initial momentum of the hockey puck is equal to the final momentum of the goalie and the puck combined. Since momentum is defined as mass times velocity, we have:
Initial momentum of the puck = Final momentum of the goalie and the puck
(0.105 kg) * (30 m/s) = (0.105 kg + 80 kg) * v
Now we can solve for v, which is the goalie's speed after catching the puck:
v = (0.105 kg * 30 m/s) / (0.105 kg + 80 kg)
v โ 0.0762 m/s
So, the goalie will slide on the ice with a speed of approximately 0.0762 m/s. Well, that's not a very impressive shot, but hey, at least the goalie caught it!