1. **State the problem:** An object Z has a kinetic energy of 800 J at point X and moves horizontally to point Y, experiencing a constant opposing force of 100 N over a distance of 2 m. We need to find the kinetic energy of Z at point Y. 2. **Relevant formula:** The work done by a force is given by $$W = F \times d \times \cos(\theta)$$ where $F$ is the force magnitude, $d$ is the displacement, and $\theta$ is the angle between force and displacement directions. 3. **Important rule:** Since the force opposes the motion, $\theta = 180^\circ$ and $\cos(180^\circ) = -1$, so the work done by the force is negative, reducing kinetic energy. 4. **Calculate work done by the force:** $$W = 100 \times 2 \times (-1) = -200 \text{ J}$$ 5. **Apply work-energy theorem:** The change in kinetic energy equals the work done: $$\Delta KE = W$$ 6. **Calculate kinetic energy at point Y:** $$KE_Y = KE_X + W = 800 + (-200) = 600 \text{ J}$$ **Final answer:** The kinetic energy of object Z at point Y is **600 J**.