A lead ball is dropped into a lake

[Phoenixtears]

Homework Statement

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?

Homework Equations

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

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

 

[LowlyPion]

Homework Statement

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?

Homework Equations

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

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

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?

 

[baba89]

I would approach this problem by first clarifying the question and making sure all the necessary information is provided. It is important to have a clear understanding of the problem before attempting to solve it. In this case, the question is asking for the depth of the lake, but the given information only includes the height of the diving board and the time it takes for the ball to reach the bottom. It does not mention the distance the ball travels horizontally before hitting the water or the angle at which it enters the water. Without this information, it is impossible to accurately determine the depth of the lake.

Assuming that the ball is dropped straight down from the diving board and enters the water at a 90 degree angle, we can use the equation X=V0*t + (at^2)/2 to solve for the total distance traveled by the ball. Since we know the initial velocity (V0=0) and the time it takes for the ball to reach the bottom (t=3), we can calculate the distance traveled in the air before entering the water. This distance will be equal to the height of the diving board (5.0m).

Once the ball enters the water, it will experience a change in velocity due to the resistance of the water. However, without knowing the mass of the ball or the force acting on it, we cannot accurately determine the velocity of the ball once it enters the water. Therefore, it is not possible to calculate the depth of the lake using the given information.

In conclusion, as a scientist, I would recommend asking for clarification on the given information or looking for other sources of information to accurately solve this problem. It is important to always consider the limitations of the given information and use logical reasoning to determine what can and cannot be accurately calculated.