Subject: homework 4 correction to solutions
Correction to problem 3.4 in K&K
(I neglected the horizontal momentum.)
The whatever-it-is explodes at the top of its trajectory, so it
has zero momentum in the z (height) direction but it has nonzero
momentum in the horizontal direction.
so it starts with horizontal momentum Mv, and then you have
3/4 M v_2 + 1/4 M v_1 = Mv, if v_2 is the velocity of the larger
piece and v_1 is the velocity of the smaller piece.
but t to go up is the same as t to go down, so if the instrument
travelled L in vt and -L in v_1 t then v_1 = -v.
so then 3/4 M v_2 = 5/4 M v which gives v_2.
Then you want L+v_2 t, which you can get from calculating t directly
or from saying that L = v t and using v_2 in terms of v.
Another way is to use the center of mass motion, and say that the
center of mass travels 2L when it lands, which is the sum of
m_1 (0) + m_2 (d_2) (where you want d_2 and the origin is at the
launch point). thanks to one of you for pointing this out!
anyhow so the right answer is 8L/3.