Two hockey pucks, labeled A and B, are initially at rest on a smooth ice surface and are separated by a distance of 26.0 m . Simultaneously, each puck is given a quick push, and they begin to slide directly toward each other. Puck A moves with a speed of 2.30 m/s , and puck B moves with a speed of 3.90 m/s .

Your answer should satisfy common sense. For instance, can you decide which of the following values for the distance covered by puck A would definitely be wrong, regardless of the speed of the two pucks and considering that the two pucks are sliding toward each other?

(A) 5 m
(B) 33 m
(C) 27 m
(D) 1 m
(E) 21 m

Since the total distance between them is 26 m, the common sense dictates that the distance traveled by each puck must be less than 26 m regardless of the speed of the two pucks.

so the options B) 33 m and C) 27 m are definitely wrong since they are greater than 26 m.

We can also easily find the distance traveled by each pucks also.

let [tex]v_{A}[/tex] and [tex]v_{B}[/tex] be the velocity of the pucks A and B respectively

[tex]v_{A}t = 26- v_{B}t\\\\2.30t = 26 - 3.90t\\\\6.2t = 26\\\\t = \frac{26}{6.2} \\\\x_{A} =v_{A}t\\\\x_{A} =2.3 \times \frac{26}{6.2}\\\\x_{A} =9.65\\\\x_{B} =v_{B}t\\\\x_{B} =3.9 \times \frac{26}{6.2}\\\\x_{B} =16.35\\[/tex]