In attempting to pass the puck to a teammate, a hockey player gives it an initial speed of 2.0m/s, but because of the kinetic friction between the puck and the ice, the puck travels only half the distance between the players before coming to rest. Assuming that the ice's friction is the same everywhere, what minimum initial speed did the player need to give the puck in order for it to reach the teammate?

Question

In attempting to pass the puck to a teammate, a hockey player gives it an initial speed of 2.0m/s, but because of the kinetic friction between the puck and the ice, the puck travels only half the distance between  the players before coming to rest. Assuming that the ice's friction is the same everywhere, what minimum initial speed did the player need to give the puck in order for it to reach the teammate?

drwls · Answer

The puck will need to do twice as much work against friction in order to travel twice as far. That means the initial kinetic energy, (1/2)MV^2, will have to be twice as high.

Since M will be the same, V must increase by a factor sqrt 2 = 1.414

The new V = 2.828 m/s