physics again! work-energy question?

Question

Any help would be appreciated!!

In attempting to pass the puck to a teammate, a hockey player gives it an initial speed of 2.0 m/s. However, this speed is inadequate to compensate for the kinetic friction between the puck and the ice. As a result, the puck travels only one-half the distance between the players before sliding to a halt. What minimum initial speed should the puck have been given so that it reached the teammate, assuming that the same force of kinetic friction acted on the puck everywhere between the two players?

Thanks!

Answer 1

Energy lost in Friction = F*d

Energy lost to go twice as far = F*2*d

Initial KE = 1/2 m (v1)^2 = F*d

Now to go twice as far

1/2 m (v2)^2= F*2*d

1/4 m (v2)^2 =F*d

therefore

1/4 m (v2)^2 = 1/2 m (v1)^2
(v2)^2 = 2* (v1)^2
(v2)^2 = 2* (2 m/sec)^2
(v2)^2 = 8 m^2/sec^2
v2=2.828 m/sec