How deep is the lake? velocity physics

[hachi_roku]

Homework Statement

a lead ball is dropped into a lake from a diving board 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 after 3s after it is released. how deep is the lake?

Homework Equations

The Attempt at a Solution

i just need a hint. i think i need to find the velocity first but i don't know how.
i'm trying to treat the problem as two different systems. first system would be from the diving board to the water, and the second system would be from the water to the ground of the lake. i can't find the velocity without the time...i need the time that it takes to hit the water but i don't know how to do that

 

[LowlyPion]

Looks like you pretty much have it.

What velocity does it strike the water with? You know h and g so ...

https://www.physicsforums.com/showpost.php?p=905663&postcount=2

How long does it take to fall 5m ? T = ... ?

So (3 - T)*V = ... your answer?

 

[thomate1]

.To find the depth of the lake, you will need to use the equation d = 1/2gt^2, where d is the depth, g is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes for the ball to reach the bottom. Since the ball reaches the bottom after 3 seconds, you can plug that into the equation and solve for d. Remember to convert the units to match (meters and seconds).

To find the velocity, you can use the equation v = gt, where v is the velocity and g is again the acceleration due to gravity. Since the ball has a constant velocity while sinking, you can use the velocity it had when it hit the water, which can be calculated using the equation v = u + at, where u is the initial velocity (in this case, 0) and a is the acceleration due to gravity. Once you have the velocity, you can use it in the equation for depth.

Hope this helps!