Question

A rock is thrown horizontally from a 125 m high cliff. It strikes the ground 100 m from the base of the cliff. At what speed was it thrown?

Group of answer choices

5.5 m/s

13.3 m/s

19.8 m/s

20.1 m/s

Answer 1

To find the speed at which the rock was thrown horizontally from the cliff, we need to analyze the motion in the vertical and horizontal directions separately.

1. **Vertical motion**: The rock is falling under the influence of gravity. We can use the following equation for vertical motion to determine the time it takes to fall 125 meters:

\[
d = \frac{1}{2} g t^2
\]

Where:
- \(d\) is the distance fallen (125 m),
- \(g\) is the acceleration due to gravity (\(9.81 \, \text{m/s}^2\)),
- \(t\) is the time in seconds.

Rearranging the equation to solve for \(t\):

\[
t^2 = \frac{2d}{g}
\]
\[
t^2 = \frac{2 \cdot 125}{9.81}
\]
\[
t^2 = \frac{250}{9.81} \approx 25.455
\]
\[
t \approx \sqrt{25.455} \approx 5.045 \, \text{s}
\]

2. **Horizontal motion**: The horizontal distance covered is given as 100 m, and horizontal motion has a constant velocity, so we use:

\[
d = v \cdot t
\]

Where:
- \(d\) is the horizontal distance (100 m),
- \(v\) is the horizontal speed (which we want to find),
- \(t\) is the time calculated above (approximately 5.045 s).

Rearranging the equation to solve for \(v\):

\[
v = \frac{d}{t} \approx \frac{100}{5.045} \approx 19.8 \, \text{m/s}
\]

Thus, the speed at which the rock was thrown is approximately **19.8 m/s**.

Therefore, the correct choice from the options is:

**19.8 m/s**.