How much does a bullet penetrate a wall?

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SUMMARY

The discussion centers on calculating the penetration depth of a bullet weighing 50g and traveling at an initial speed of 300m/s when it strikes a wall, with a force of 70N acting on it. Participants emphasize the importance of understanding the relationship between speed, acceleration, and time to solve the problem effectively. The problem requires calculus to analyze the time-dependent force acting on the bullet, and a comparison with a constant force scenario is suggested for clarity.

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Homework Statement


A bullet weighing m = 50g with a initial speed of v = 300m/s hits a wall. The wall is build in a way that the value of the force it causes on the bullet is given by:
aTdKzyA.png
. The time starts after the bullet hits the wall and F0 = 70N. How much does the bullet penetrate the wall, in centimeters?


Homework Equations


Force made by the wall on the bullet =
aTdKzyA.png



The Attempt at a Solution


My first thought was: to determine the distance I need the time, initial speed, final speed and aceleration, depending on the equation. So, I tried to find the time. Failed. Then I tried to find the aceleration... failed. Note that I'm just beginning and my high-school wasn't that great, so I'm having some troubles with exercises like this.
 
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The problem involves calculus if you're up to that at least.

Can you set up a relationship between speed and acceleration?
 
This is a tricky problem, so it is very important that you really think about how to approach it instead of just trying different things. Can you describe what is physically happening here?

It would be a useful exercise to solve for the case with a constant force for comparison. Then determine what you need to do differently due to the time-dependent force.
 

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