# The Motion of the Center of Mass

1. Homework Statement

A projectile is launched with speed v0 at an angle theta 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 further from the launch point than the point directly below the explosion at time (t < v0 sin(theta) / g) after the explosion. How high does the other piece go? Where does the other piece land? Answer in terms of v0, theta, D, and t.

2. Homework Equations

Conservation of momentum
$v = v_0 + a t$
$x = x_0 + v_0 t + (1/2) a t^2$
$v^2 = v_0^2 + 2 a \Delta x$
Others?

3. The Attempt at a Solution

I started out by drawing a picture of the particles. I assume since the first particle hits the ground at less than half of the time of flight, it must have been directed downward. I set up conservation of momentum formulae for both the x and y directions:
$2 v_0 cos\theta = v_1 cos\theta_1 + v_2 cos\theta_2$
$0 = v_1 sin\theta_1 + v_2 sin\theta_2$
Also:
$v_1 cos\theta_1 = \frac{D}{t}$
I'm not sure where to go from here. All attempts seem to lead to dead ends. Any help is appreciated. Thanks!

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