Question

A key falls from a bridge that is 44 m above the water. It falls directly into a model boat, moving with constant velocity, that is 19 m from the point of impact when the key is released. What is the speed of the boat

Answer 1

The time $t$ it takes for the key to fall 44 m is

$44\,\mathrm m=\dfrac12\left(9.8\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2\implies t=3.0\,\mathrm s$

(notice I'm taking the downward direction to be positive)

The boat, moving at a presumably constant speed, then has 3.0 s to travel 19 m to the point of impact, which means its speed must be

$v=\dfrac{19\,\mathrm m}{3.0\,\mathrm s}=6.3\,\dfrac{\mathrm m}{\mathrm s}$