# Homework Help: Surprising Exploding Firework

1. Nov 6, 2006

### kenau_reveas

A mortar fires a shell of mass m at speed v0. The shell explodes at the top of its trajectory (shown by a star in the figure) as designed. However, rather than creating a shower of colored flares, it breaks into just two pieces, a smaller piece of mass 1/5 m and a larger piece of mass 4/5 m. Both pieces land at exactly the same time. The smaller piece lands perilously close to the mortar (at a distance of zero from the mortar). The larger piece lands a distance d from the mortar. If there had been no explosion, the shell would have landed a distance from the mortar. Assume that air resistance and the mass of the shell's explosive charge are negligible.

Find the distance d from the mortar at which the larger piece of the shell lands.

Express d in terms of .

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2. Nov 6, 2006

### srnj222

The center of mass of the shell will continue on the initial trajectory:

cm = ((1/5)m*0 + (4/5)m*d)m

cm = (4/5)d

d = (5/4)cm where cm is the position it owuld have landed at

3. Nov 6, 2006

### kenau_reveas

it says express d in terms of r. is this d is in terms of r?

4. Nov 6, 2006

### srnj222

if r is the position it would have landed at