To determine the speed at which the heavy object was thrown horizontally from the cliff, we can analyze the motion in two dimensions: vertical and horizontal.
### Step 1: Analyze the vertical motion
The vertical motion is influenced by gravity. The formula for the vertical distance \( h \) fallen after time \( t \) is given by:
\[
h = \frac{1}{2} g t^2
\]
Where:
- \( h = 23 \) m (the height of the cliff)
- \( g \approx 9.81 \) m/sĀ² (acceleration due to gravity)
Rearranging this formula to find time \( t \) gives us:
\[
t^2 = \frac{2h}{g}
\]
\[
t = \sqrt{\frac{2h}{g}}
\]
Plugging in the values:
\[
t = \sqrt{\frac{2 \times 23}{9.81}} \approx \sqrt{\frac{46}{9.81}} \approx \sqrt{4.688} \approx 2.17 \text{ s}
\]
### Step 2: Analyze the horizontal motion
The horizontal distance \( d \) traveled is given by the formula:
\[
d = v_x t
\]
Where:
- \( d = 73 \) m (the horizontal distance from the base of the cliff)
- \( v_x \) is the horizontal speed, which we need to find.
Rearranging the formula to solve for \( v_x \):
\[
v_x = \frac{d}{t}
\]
Substituting the values into the equation gives:
\[
v_x = \frac{73}{2.17} \approx 33.65 \text{ m/s}
\]
### Conclusion
The speed at which the heavy object was thrown horizontally is approximately **33.65 m/s**.