Question

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

Answer 1

B) 33 m C) 27 m

Step-by-step explanation:

considering that the two pucks are sliding toward each other we can understand that they are on a collision course.

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
`v_(A)` and
`v_(B)` be the velocity of the pucks A and B respectively

`v_(A)t = 26- v_(B)t\\\\2.30t = 26 - 3.90t\\\\6.2t = 26\\\\t = (26)/(6.2) \\\\x_(A) =v_(A)t\\\\x_(A) =2.3 * (26)/(6.2)\\\\x_(A) =9.65\\\\x_(B) =v_(B)t\\\\x_(B) =3.9 * (26)/(6.2)\\\\x_(B) =16.35\\`