An object is dropped trom a tower, 1600 Htab the object's volocity at the moment of impact? It takes \( \square \) sec for the object to hit the groun (Round to the nearest tenth as needed.)

To solve this problem, we'll use the principles of free fall under the influence of gravity. Here's a step-by-step breakdown: ### Given: - **Height (h)** = 1600 feet - **Initial velocity (u)** = 0 ft/s (since the object is dropped) - **Acceleration due to gravity (g)** = 32 ft/s² ### To Find: 1. **Time (t)** it takes for the object to hit the ground. 2. **Velocity (v)** at the moment of impact. ### 1. Calculating the Time (t): We use the equation for the distance covered under constant acceleration: \[ h = \frac{1}{2} g t^2 \] Plugging in the known values: \[ 1600 = \frac{1}{2} \times 32 \times t^2 \] \[ 1600 = 16 t^2 \] \[ t^2 = \frac{1600}{16} = 100 \] \[ t = \sqrt{100} = 10 \text{ seconds} \] ### 2. Calculating the Velocity (v) at Impact: We can use the equation: \[ v = g t \] Plugging in the known values: \[ v = 32 \times 10 = 320 \text{ ft/s} \] ### **Final Answers:** - **Time to hit the ground:** \( \boxed{10.0\ \text{seconds}} \) - **Velocity at impact:** \( \boxed{320\ \text{ft/s}} \)