Question

A man throws a rock horizontally off a building with an initial velocity of 23.1 m/s. It hits the ground 95.6 m from the building. How tall is the building? (Report your answer as a positive value.)

Answer 1

Question

Given:

$$s = 95.6 \text{ m}$$ $$v = 23.1 \frac{\text{m}}{s}$$

Need to find: $h$.

Solving:

$$s = v \cdot t \Rightarrow t = \frac{s}{v}.$$ $$h = \frac{g t^2}{2} = \frac{g s^2}{2 v^2}$$

According to the given data we will have:

$$h = \frac{g s^2}{2 v^2} = \frac{9.8 \cdot (95.6)^2}{2 \cdot (23.1)^2} = 83.9 \text{ m}.$$

Answer: 83.9 meters.