ghostanime2001 said:
Before Jump = After jump (rabbit jumps from left plate to right plate)
[itex]\left(m+m_{R}\right)v_{i}=m_{R}v_{R}-mv_{f}[/itex]
[itex]0=m_{R}v_{R}-mv_{f}[/itex]
[itex]mv_{f}=m_{R}v_{R}[/itex]
I don't understand why this equation if solved for v[itex]_{f}[/itex] gives a positive value. I have followed the sign conventions in the first line, but I do not understand why it works out to give a positive velocity instead of a negative velocity.
It comes out positive because you have already included the minus sign in your equation. Your v
f is the
magnitude of the velocity. If you want the sign of v
f to be negative (letting the solution provide the proper sign), you would have just done:
[itex]\left(m+m_{R}\right)v_{i}=m_{R}v_{R} + mv_{f}[/itex]
[itex]0=m_{R}v_{R} + mv_{f}[/itex]
[itex]mv_{f}= -m_{R}v_{R}[/itex]
Which would give you a negative value.
Personally, I would have done it the way you did, letting v
f in your equation just stand for the magnitude. (It's easier to work with variables that you know will be positive when you know the direction.)
Even though your variable is positive, the actual momentum is of course negative.
The second conservation of momentum equation of left plate (second jump from right plate back to left plate):
Before landing = After landing
[itex]-mv_{f}-m_{R}v_{R}=-(m+m_{R})v[/itex]
Once again, you have incorporated the direction of the various momenta by adding minus signs in your equation, thus your values for v
f, v
R, and v are all positive.