im only given on number how can i solve this ... hate to ask two physics ?'s but im very confused?

Question

ok im only given intial speed so im not sure how to solve this....

a hockey player fives a speed 1.9 m/s to puck. this is inadequate b/c kinetic friction. as result puck goes 1/2 distance between players before stopping. what is minimum initial speed taht should have been given to puck that that is would have reached teammate???

i dont even know where to begin with this problem... please explain.... in detail

Answer 1

Let the distance to teammate be D. Using the equation
Vf^2 = Vo^2 + 2*a*s
to study the first attempt, we can find what a is. Vf=0 because it slid to a stop. Vo is the 1.9 m/s it started with, s=D/2, the distance it traveled before stopping. Filing in what we know
0 = (1.9 m/s)^2 + 2*a*D/2
a = -(1.9 m/s)^2 / D = -3.6/D m^2/s^2

This value a will still be the sliding deceleration if the puck is hit harder. So using the same motion equation where we now know a, Vf is still 0, s = D (it stops at the teammate), and Vo is the new unknown
0 = Vo^2 + 2*(-3.6/D m^2/s^2)*D
Vo^2 = 7.2 m^2/s^2
Vo = 2.7 m/s will just get the puck there.