Hockey puck!?

Question

http://img174.imageshack.us/img174/7853/lastscanxz1.jpg

My text book says 7.3 x 10^3 m/s^2 [7.5 N of W]
I assumed the answer was rounded but the answer i got was in a totally different direction.

The answer in the book is exactly as I typed, what i got was:

7281 m/s^2 @ [14.6 degrees W of N]

*rounded some of the answers I got.

Answer 1

Either you typed the direction in incorrectly, or the book has a serious misprint. The acceleration was in a direction:

14.75... degrees W of N.

(You can tell it has to be MOSTLY in a NORTHERLY direction because the impact ALMOST reverses the souhtbound component, while only SLIGHTLYreducing the eastbound component. So the impulse/acceleration has a much larger NORTHERLY component than its WESTERLY component!)

The change in velocity component in the EASTERN direction is (21 - 26) cos (22 degs) m/s, that is it's 5 cos 22 m/s in the WESTERN direction = 4.635919... m/s.

In the NORTHERLY direction it's [21 - (-26)] sin 22 m/s, that is 47 sin 22 m/s = 17.60651... m/s

So the direction of the change is W of N by
Tan^(-1) [4.635919... / 17.60651...] = Tan^(-1) 0.263307... = 14.7516... degrees, as given above.

The total magnitude of the change is sqrt (4.635919...^2 + 17.60651...^2)

= 18.2066... m/s.

It occured in 2.5 ms, that is in 2.5 x 10^(-3) ms, so the average acceleration (from delta v = a_av delta t) = 18.2066... X 10^3 m/s / 2.5 s = 7.2826... x 10^3 m/s^2.

VERY CURIOUS! The answer given (7.3 x 10^3 m/s^2) is exactly my result, rounded to two sig. figs., but the DIRECTION given seems to be completely SCREWY (a technical term we in the physics/astrophysics trade use on finding such discrepancies).

I agree with you that as far as the direction of the acceleration is concerned, the book's answer is COMPLETELY UNACCEPTABLE --- not only because of what I fully worked out, but also because of what I said above on quite general grounds. It is ABSOLUTELY clear that the dominant change is in essentially REVERSING the southern component of velocity, which means that the average acceleration must be DOMINATED by a northerly component. The book's answer, that it's dominated by a WESTERLY component, is SIMPLY ABSURD.

Someone made a significant Boo-boo!

Live long and prosper.