1. **Problem:** Find the time it will take for the cannonball to reach the ground given the height equation $$h = -16t^2 + 128t$$. 2. **Formula and rules:** The cannonball reaches the ground when height $$h = 0$$. 3. **Set the equation to zero:** $$-16t^2 + 128t = 0$$ 4. **Factor the equation:** $$t(-16t + 128) = 0$$ 5. **Solve each factor:** - $$t = 0$$ (initial time) - $$-16t + 128 = 0$$ 6. **Solve for $$t$$ in the second equation:** $$-16t + 128 = 0$$ $$-16t = -128$$ $$\cancel{-16}t = \cancel{-128}$$ $$t = \frac{128}{16} = 8$$ 7. **Answer:** The cannonball will hit the ground after $$8$$ seconds. --- **Slug:** cannonball time **Subject:** physics **svg:** "" **desmos:** {"latex":"h=-16t^2+128t","features":{"intercepts":true,"extrema":true}} **q_count:** 3