Question

A stone is dropped from the top of a cliff. It hits the ground after 55 s. How high is the cliff?

Answer 1

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:

\[
\boxed{14826.125 \, \text{m}}
\]