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.
- 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 \(t\):
\[ t^2 = \frac{2d}{g} \] \[ t^2 = \frac{2 \cdot 125}{9.81} \] \[ t^2 = \frac{250}{9.81} \approx 25.455 \] \[ t \approx \sqrt{25.455} \approx 5.045 , \text{s} \]
- 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.
1 answer