How deep is the lake? velocity physics

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SUMMARY

The discussion focuses on calculating the depth of a lake based on the motion of a lead ball dropped from a height of 5.0 meters. The ball enters the water and sinks at a constant velocity equal to its impact velocity, reaching the bottom after 3 seconds. To find the lake's depth, participants suggest determining the impact velocity using the equation of motion under gravity and then applying the time taken to sink to calculate the total depth.

PREREQUISITES
  • Understanding of kinematic equations for free fall
  • Knowledge of gravitational acceleration (g = 9.81 m/s²)
  • Ability to solve for time and velocity in physics problems
  • Familiarity with the concept of constant velocity motion
NEXT STEPS
  • Calculate the impact velocity of the ball using the equation v = √(2gh)
  • Determine the time taken to fall 5 meters using T = √(2h/g)
  • Apply the total time of 3 seconds to find the depth using the formula depth = (3 - T) * V
  • Explore additional physics concepts related to motion in fluids
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and fluid dynamics, as well as educators seeking to enhance their teaching methods in these areas.

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?


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
 
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