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Free Fall in One Dimension

Example: A climber standing on the edge of a cliff throws a rock vertically downward. The initial velocity of the rock is $14\frac{m}{s}$ . If the rock reaches the ground 3 seconds later, how tall is the cliff?

Draw a picture:

Given:

$v_{i}=14\ \frac{m}{s}$
$g=9.81\ \frac{m}{s}$
$t=3\ s$
$h_{f}=0\ m$

Unknown:

$h_{i}=?$

Standard distance equation: $h_{f}=h_{i}+v_{i}t+\frac{1}{2}gt^{2}$

Solve for $h_{i}$

$h_{f}-v_{i}t-\frac{1}{2}gt^{2}=h_{i}$

$(0\ m)-(-14\ \frac{m}{s})(3\ s)-(\frac{1}{2})(-9.81\ \frac{m}{s^2})(3\ s)^{2}=h_{i}$

$h_{i}=86.14\ m=height\ of\ the\ cliff$