Question

A student drops a rock from a bridge to the
water 12.4 m below.
With what speed does the rock strike
the water? The acceleration of gravity is
9.8 m/s^2

.
Answer in units of m/s

Answer 1

The speed of the rock, according to the gravitational acceleration is $v = g t$. The time it takes to fall from given height $h = 12.4 m$ is $t = \sqrt{\frac{2 h}{g}}$(which is found from the equation of motion $y(t) = h - \frac{g t^2}{2}$ by equating $y$ to zero and solving for t).

Hence, substituting the time into the equation for speed, obtain $v = g t = g \sqrt{\frac{2 h}{g}} = \sqrt{2 g h} \approx 15.6 s$.