Going Crazy Exploding Projectiles

[jessicak]

1. Homework Statement

A projectile is launched with speed v0 at an angle with respect to the horizontal. At the peak of its motion, it explodes into two pieces of equal mass, which continue to move in the original plane of motion. One piece strikes the ground a horizontal distance D farther from the launch point than the point directly below the explosion at a time t<v0sin/g. How high does the other piece go? Answer in terms of v0, , g, and t.

2. Homework Equations
m1v1=m2v2
h=v02sin2(/g


3. The Attempt at a Solution
I know I should be doing a momentum balance in the vertical direction before and after the collision, but I'm struggling to get the right equation. Any help would be appreciated

 

[jbsteele]

. Let v1 be the vertical velocity of the piece that reaches the ground and v2 be the vertical velocity of the piece that goes higher. Before the collision:m1v1sin=m2v2sinAfter the collision:m1(v1sin-gt)=m2(v2sin)Solve for v2sin:v2sin=m1(v1sin-gt)/m2Now plug in for v2sin to find h:h=(v02sin2-2gtv0sin+gt2)/g