Answer
4900 m/s.
Work Step by Step
The momentum in the horizontal direction will be conserved. Let the positive direction be the direction in which the alpha particle moves. The initial momentum is zero.
$$0 = (57 M)(v) + (M)(2.8 \times 10^5 \frac{m}{s})$$
Solve for velocity v = -4900 m/s, rounded to 2 significant figures.
The negative sign means the nucleus is moving in the opposite direction as the alpha particle.
The speed is 4900 m/s.
