4- a key falls from a bridge that is 45 m above the water. it falls directly into a model boat, moving with…

4- a key falls from a bridge that is 45 m above the water. it falls directly into a model boat, moving with constant velocity, that is 12 m from the point of impact when the key is released. what is the speed of the boat?

4- a key falls from a bridge that is 45 m above the water. it falls directly into a model boat, moving with constant velocity, that is 12 m from the point of impact when the key is released. what is the speed of the boat?

Answer

Explanation:

Step1: Calculate time for key to fall

We use the free - fall equation $h = \frac{1}{2}gt^{2}$, where $h = 45m$ and $g=9.8m/s^{2}$. Rearranging for $t$, we get $t=\sqrt{\frac{2h}{g}}$. $t=\sqrt{\frac{2\times45}{9.8}}\approx\sqrt{\frac{90}{9.8}}\approx 3.03s$

Step2: Calculate speed of boat

The boat moves a distance $d = 12m$ in time $t$. The speed $v$ of the boat is given by the formula $v=\frac{d}{t}$. $v=\frac{12}{3.03}\approx 3.96m/s$

Answer:

$3.96m/s$