... physics.

I cannot seem to get this for the effing life of me, and would appreciate some help if anyone's available.

- A bullet traveling horizintally at a speed of 350m/s hits a board perpendicular to the surface, passes through it and emerges ont he other side at a speed of 210m/s.
If the board is 4.00cm thick, how long does the bullet take to pass through it?

I know once someone shows/tell me this, I'm gonna feel like an idiot.

So... TIA! :o

 

I'm just gonna take a wild guess.. 0.0001538 seconds.. ? lol, I'm no physicist, but this sounds possible?

(4cm/35000cm/s) + (4cm/21000cm/s) /2 = 0.0001538 seconds

I barely passed algebra.. so don't take my word for it..

 

do what i do. call the best looking girl (thats smart ofcourse) i can think of and have her do it for me.

 

You have to use your kinematics formulas for simple mechanical equations. Assuming the board has a constant resistance throughout the entire penetration of it, you can figure it out like this.

Here's the kinematic formula I'm going to use right here

X = ½ at² + vt + x

X = distance traveled
a = acceleration
t = time
v = starting velocity
x = starting position

Just fill in the equation with what you have and you get this

0.04 = ½ at² + 350t + 0


Now you may think "oh s*** we're missing two variables" but to find out what the acceleration is we use this kinematic formula here

v² = Vnot² + 2aX

v = final velocity
Vnot = original velocity
a = acceleration
X = distance traveled

Fill it in and we get this:

210² = 350² + 2(a)(0.04)

44,100 = 122,500 + 0.08a

-78,400 = 0.08a

-980,000 = a


Now lets go back to the first kinematic formula and do this:

0.04 = ½ (-980,000)t² + 350t + 0

0 = 490,000t² +350t - 0.04

Now what does that remind you of? Yep that's right, the quadratic formula. Throw this into the quadratic formula and you get this:

t = 0.00010022
t = -0.00081451

Obviously in this equation, the variable for t can't be negative, so your answer is...





Drum roll please.








It takes 0.00010022 seconds for the bullet to pass through the board.

 

wow.. well I was really close..

 

i think of simple as maybe addition, subtraction, multiplication, division, and square roots. that problem does not fall any where into my definition of simple

 

.00014286

 

I couldn't even read that.

 

I'm glad im not alone! lol I got a headache from trying to understand that.

Answer: The bullet goes through the wood really fast.

 

That's what I get, too, without using any fancy formulas.

350 + 210 = 560, divide by 2 = average speed of 280 fps when it passes through the board.

.04/280 = .00014286.

 

Somebody paid attention in class! Well done.

Addition, subtraction, multiplication, division and square roots were the only things used! Therefore, by your own admission, the problem was easy!

Edited to add, he used substitution as well, my bad.

- NCSU

 

Might seem like the way to go, except the tip of the bullet doesn't hit the wood and immediately slow down to 280m/s, pass through the wood at that constant speed, then slow down to 210m/s when it exits the wood. Make sense?

Yeah, it happens really fast, but between 0.000100 and 0.000142 there's a 40% difference. Like saying someone was going 100mph when they were really going 140mph.

- NCSU

 

Absolutely. I just did not know the formulas and figured my method would end up being pretty close.

I am surprised that the difference is 40%. Probably because the change is speed is so great and the distance is so small.

 

Yeah we are talking about some very extreme variables here. 4CM is a VERY short distance, and the bullet is traveling about 780MPH, then slows down to about 470MPH in that distance. Those are some crazy amounts of force being transferred.

Needless to say this series of events is only replicable on paper.

 

Oh Jesus! Math! I'm out of here!