To find the height of the cliff from which the stone is dropped, we can use the kinematic equation for an object in free fall. The equation is:
\[ h = \frac{1}{2} g t^2 \]
where:
- \( h \) is the height (in meters),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( t \) is the time (in seconds).
In this case, the stone is dropped, so \( t = 55 , \text{s} \).
Now, we can substitute the values into the equation:
\[ h = \frac{1}{2} \times 9.81 , \text{m/s}^2 \times (55 , \text{s})^2 \]
Calculating \( (55 , \text{s})^2 \):
\[ (55 , \text{s})^2 = 3025 , \text{s}^2 \]
Now substituting back into the height equation:
\[ h = \frac{1}{2} \times 9.81 , \text{m/s}^2 \times 3025 , \text{s}^2 \]
Calculating the multiplication:
\[ h = 0.5 \times 9.81 \times 3025 \]
Calculating \( 9.81 \times 3025 \):
\[ 9.81 \times 3025 = 29652.25 \]
Then multiplying by \( 0.5 \):
\[ h = 0.5 \times 29652.25 = 14826.125 , \text{m} \]
Thus, the height of the cliff is approximately:
\[ \boxed{14826.125 , \text{m}} \]
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