- #1

Kermit_the_Phrog

- 22

- 3

- Homework Statement:
- In Fig below, a mobile cannon of mass M=1300 Kg fires a ball of mass m=72 kg in the positive direction of an x axis, at velocity Vbc= 55 m/s relative to cannon. Because of the firing, the cannon recoils (moves) with velocity Vcg relative to the ground. What are the magnitude and direction of Vcg?

- Relevant Equations:
- Pi=Pf

Since Pi = Pf,

0 = MbVbg + McVcg

I just need to express Vbg in terms of Vbc and Vcg (that is, I need to express the velocity of the ball relative to the ground in terms that I know/want to solve for):

by reference frames:

Vbc = Vbg + Vcg

so Vbg = Vbc -Vcg

Now I can sub in and solve

0 = MbVbg + McVcg

0 = Mb(Vbc -Vcg) + McVcg

0 = MbVbc - MbVcg +McVcg

MbVcg - McVcg = MbVbc

Vcg(Mb - Mc) = MbVbc

therefore,

Vcg = 72*55/(72-1300)

= -3.2 m/s

which would be a.

HOWEVER the teacher's answer key states that the answer is b, -2.9 m/s.

this answer is obtained if the denominator was " (- mb - mc) ".

Thus, did I just mess up somewhere with my signs? I can't find mistake, and any help deducing this would be appreciated, as I was pretty confident about my answer until seeing that it was wrong.