# A key falls from a bridge that is 50 m above the water. It falls directly into a model boat, moving with constant velocity, that is 18 m from the point of impact when the key is released. What is the speed of the boat ?

Sep 12, 2015

The speed of the boat is $\text{5.6 m/s}$.

#### Explanation:

The ky to this problem is the fact that the boat must travel 18 m in the same time the key takes to falls from a height of 50 m.

Assuming that the key is free falling, you can say that

h = underbrace(v_0)_(color(blue)("=0)) * t + 1/2 * g * t^2

$h = \frac{1}{2} \cdot g \cdot {t}^{2}$

Since the boat moves with constant velocity, you can say that

$v = \frac{d}{t}$

Use the first equation to find the time needed for the key to reach the water, which must be equal to the time needed for the boat to get into position

t = sqrt((2 * h)/g) = sqrt((2 * 50color(red)(cancel(color(black)("m"))))/(9.8color(red)(cancel(color(black)("m")))/"s"^2)) = "3.20 s"

This means that the speed of the boat must be

v = "18 m"/"3.20 s" = color(green)("5.6 m/s")