Homework Help: Bowling ball dropped into water, find velocity as it strikes the bottom

1. Sep 9, 2011

bbraves7

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

A bowling ball is dropped from a boat so that it strikes the surface of a lake with a speed of 25 ft/s. Assuming the ball experiences a downward acceleration of a=10-.9v2 when in the water, determine the velocity of the ball when it strikes the bottom of the lake.

2. Relevant equations

v0=25 ft/s
da/dt=v
dv/dt=y

3. The attempt at a solution

I've tried this problem a few different ways, the first by substituting v into the given a=10-.9v2 and then integrating, but that does not work because v0 is the initial velocity and not the velocity as it travels through the water, which obviously will change based on the acceleration. I think I am missing that the ball will slow down as it is in the water, and thus the acceleration will slow down according to the velocity at that time. I just can't seem to put that into the form of any equations I'm familiar with. I have the solutions manual for this textbook, but the way they solve it they include an equation a=10-.9v2=k(c2-v2) but I don't know where they pulled that from because I can't find anything close to that in the text. I desperately want to comprehend this problem rather than just regurgitate the solution. Any help will be greatly appreciated.

2. Sep 9, 2011

lewando

Some thoughts:
You probably meant dv/dt=a, dy/dt=v.

You are given V0 and a, but not the depth of the lake, which should be specified.

a=10-.9v2, has units in m/s2? ft/s2?

I think the intent of specifying the acceleration that way is to indicate a terminal velocity (when a = 0). Though, if this is a very shallow lake, it may not reach terminal.

3. Sep 9, 2011

bbraves7

Sorry, it was very late last night when I posted this problem.

I meant to put dy/dt=v, dv/dt=a.

The depth of the lake is 30m. v0= 25ft/s.

Sorry again about that. I had been working on this for about two hours so my brain was fried.