1. **State the problem:** A cannon of mass 1445 kg fires a cannonball of mass 4.6 kg horizontally with velocity -356 m/sec. We need to find the recoil velocity of the cannon. 2. **Relevant principle:** Use conservation of momentum, which states total momentum before firing equals total momentum after firing. 3. **Set up the equation:** Let $v_c$ be the recoil velocity of the cannon. Initial total momentum = 0 (both at rest) Final total momentum = momentum of cannonball + momentum of cannon $$0 = m_{ball} \times v_{ball} + m_{cannon} \times v_c$$ 4. **Substitute known values:** $$0 = 4.6 \times (-356) + 1445 \times v_c$$ 5. **Solve for $v_c$:** $$1445 \times v_c = -4.6 \times (-356)$$ $$1445 \times v_c = 1637.6$$ 6. **Divide both sides by 1445:** $$v_c = \frac{1637.6}{1445}$$ 7. **Simplify fraction:** $$v_c = \frac{\cancel{1637.6}}{\cancel{1445}} \approx 1.134$$ 8. **Interpretation:** The recoil velocity of the cannon is approximately 1.134 m/sec in the positive direction (opposite to the cannonball's velocity). **Final answer:** $$v_c = 1.134$$