# A lead ball is dropped into a lake

1. Aug 29, 2008

### Phoenixtears

1. The problem statement, all variables and given/known data

A lead ball is dropped into a lake from a diving baord 5.0m above the water. After entering the water, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the water. The ball reaches the bottom 3.0 s after it released. How deep is the lake?

2. Relevant equations
at-V1= -V2
X=V0*t + (at^2)/2
(V1)^2= V0^2 + 2ax

3. The attempt at a solution
Really, aside from finding variables, I need help with the question itself. I'm having a huge debate with another student in the class about what the problem means. I take it as if the velocity increases during the fall towards the water, and then the ball slows drastically (due to the force against the ball by hitting the water) and then the ball stays consisten in the water. Though should I take into account the laws of nature that I know, even though it's introductory? The other student believes that the velocity is constant throughout the entire trip down. Meaning that when it hits the water it stays constant. Could it be a mix of these two? Perhaps the velocity increases and then stays constant after hitting the water?

The variables I already have are a= -9.8 m/s/s, and t=3. Now this is where I'm having trouble, delta-x cannot equal -5 for that is only part the way down. So I'm left with two solid variables where I need three to solve each equation. Suggestions?

~Phoenix

2. Aug 29, 2008

### LowlyPion

You should take the problem in 2 parts. The weight drops to the surface of the water accelerated by gravity. How long does that take to hit the surface? What speed is the ball going at that point?

Next part knowing speed and knowing how much time remains in your time budget of 3 seconds ... let's see you have speed and you have time ... any idea on how to figure distance?