A bullet ricochets off a steel plate problem

[Deckname]

Homework Statement

What's the median resisitive force the plate offers against the bullet given the following info? (in the picture attached)

Relevant Equations

none have been given, most likely $F_{avg}=\frac{\Delta p}{\Delta t}$

I have calculated KE_i and KE_f, took the difference between the initial and final kinetic energy of the bullet to be equal to the work spent to overcome the friction, and divided it by the distance traveled, but arrive at around 20000N. The solution should be 9.5*10^7.

Not sure what else to try at this point. Suggestions or hints please? Also this is a part of my second year mechanics seminar, and I wouldn't be asking for the solution or anything here unless passing the subject literally depended on it, as missing even 1 solution out of the 29 exercises I've already solved, it's still counted a fail. So please lend a hand!

 

[phinds]

your handwritten stuff is (1) not really acceptable for this forum and (2) not readable even if it were.

 

[Deckname]

Alright, thanks for pointing that out, I won't post handwritten stuff again. But then again I've explained what I've done in the OP (forgot to add I divided the work by distance, since F=W/d) and I've also attached a picture of the problem itself that I made in paint to be clearly readable.

 

[Nugatory]

What is the change in the bullet’s momentum?

 

[Deckname]

What is the change in the bullet’s momentum?

Alright, I now realize I'm supposed to calculate the solution through F_avg=ΔP/Δt, but how do you calculate the change in momentum when not only the momentum changed, but also it's direction? I'm confused now.

 

[Deckname]

I've used the $F_{avg}=\frac{\Delta P}{\Delta t}$ and have arrived at the same result of ~$20000N$. I have calculated $\Delta t$ by using $v^2={v_0}^2+2a \Delta x$ to calculate the acceleration and plugged it in $t=\frac{\Delta v}{a}$ to get time. I calculated $\Delta p$ by taking into consideration the velocity vectors parallel to the trajectory of the bullet, since this is the change in momentum we want to consider, and I then plugged all of that into the first equation I mentioned, $F_{avg}$, and got $20000N$ again.

I'm actually confused now, am I constantly making a mistake in all the different ways this can be solved, since I keep arriving at the almost identical result (different but a few hundreds of N), or is the result my professor has provided wrong?

 

[haruspex]

I've used the $F_{avg}=\frac{\Delta P}{\Delta t}$ and have arrived at the same result of ~$20000N$. I have calculated $\Delta t$ by using $v^2={v_0}^2+2a \Delta x$ to calculate the acceleration and plugged it in $t=\frac{\Delta v}{a}$ to get time. I calculated $\Delta p$ by taking into consideration the velocity vectors parallel to the trajectory of the bullet, since this is the change in momentum we want to consider, and I then plugged all of that into the first equation I mentioned, $F_{avg}$, and got $20000N$ again.

I'm actually confused now, am I constantly making a mistake in all the different ways this can be solved, since I keep arriving at the almost identical result (different but a few hundreds of N), or is the result my professor has provided wrong?

You are still misunderstanding change in momentum. Momentum is a vector, obtained by multiplying mass by the velocity vector. The change in momentum is the change in the vector. You are only looking at change in speed and energy, which are scalars.
E.g. in an elastic bounce there is no change in speed or energy but maybe a substantial change in velocity and momentum.

To get the duration of the change (Δt), assume the frictional force is constant and find the time for the given drop in tangential velocity.