So I'm doing a simple Physics homework problem, and I'm honestly unsure if I'm using the proper formulas for each step. The problem is as follows:
A key falls from a bridge that is 47 m above the water. It falls directly into a model boat, moving with constant velocity , that is 15 m from the point of impact when the key is released. What is the speed of the boat?
I used the intial formula (to find the time it takes for the key to fall) of: $x-x_{0} = v_{0}t+\frac{1}{2}at^{2}$ and the result I got was about 3.10 seconds (it was actually 3.097...but I rounded)
Then I used the formula $x-x_{0} = \frac{1}{2}(v_{0}+v)t$ to solve for velocity of the boat - getting 9.7 m/s, but apparently this answer is incorrect. I'm sure it's probably because I'm not using the proper formula for the second step (of finding the speed of the boat) but I'm not sure which one to use (as the only information I have is time and distance). Could anyone point me in the right direction?
You found the time correctly. Now, in that same time, the boat travels $15$m. So, $$x=vt$$ $$15=v(3.1)$$
You get $v=4.84$m/s. Is that correct?