Physics H7a:
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.