How deep is the lake? velocity physics

AI Thread Summary
To determine the depth of the lake, first calculate the velocity of the lead ball as it strikes the water using the height of the diving board (5.0m) and gravitational acceleration. The time taken to fall can be found using the equation for free fall. After entering the water, the ball sinks at a constant velocity for 3 seconds, which is the total time from release to reaching the bottom. The depth of the lake can be calculated by multiplying the sinking time (3 seconds minus the fall time) by the velocity at which the ball struck the water. This approach effectively combines the two phases of the ball's motion to find the lake's depth.
hachi_roku
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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?


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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
 
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