Conservation of Linear Momentum Practice Test

A firework of mass $3.0,\text{kg}$ moves horizontally at $+4.0,\text{m/s}$ (no air resistance). It explodes into two pieces: piece 1 has mass $1.0,\text{kg}$ and piece 2 has mass $2.0,\text{kg}$. Immediately after, piece 2 moves at $+1.0,\text{m/s}$. With external impulse negligible, momentum is conserved: $\vec p_i=(3.0)(+4.0)\hat\imath$ and $\vec p_f=(1.0,\vec v_1+2.0\cdot +1.0\hat\imath)$. Calculate the velocity of piece 1 after the event given the initial conditions.

A $3.0,\text{kg}$ cart moving at $\vec v_i=+2.0,\text{m/s},\hat\imath$ explodes into two pieces of $1.0,\text{kg}$ and $2.0,\text{kg}$. The $1.0,\text{kg}$ piece leaves at $\vec v_1=+8.0,\text{m/s},\hat\imath$. With external impulse negligible, calculate the $2.0,\text{kg}$ piece’s velocity.