# Momentum and Projectile Motion

1. Dec 1, 2006

1. The problem statement, all variables and given/known data
Can anyone help me with this problem?

A bullet of mass m is moving horizontally with speed Vo when it hits and embeds in a block of mass 100m that is at rest on a horizontal frictionless table (in the diagram it isn't placed at the edge of the table, i don't know if this matters). The surface of the table is a height h above the floor. After the impact the bullet and the block slide off the table and hit the floor a distance x from the edge of the table.

Derive expressions for the following quantities in terms of m, h, Vo and appropriate constants.
a.) the speed of the block as it leaves the table
b.) the change in kinetic energy of the bullet-block system during the impact
c.) the distance x

Suppose that the bullet passes through the block instead of remaining in it.
d.) state whether the time it takes the block to reach the floor from the edge of the table would now be greater, less, or the same
e.) state whether the distance x would now be greater, less, or the same

3. The attempt at a solution
i don't think i solved these right at all...

a.) mVo = (m+100m)Vf
Vf = (mVo)/(m+100m)

b.) KEf - KEi = change in KE
1/2(m+100m)(Vf)^2 - 1/2mVo^2 = change in KE

c.) x = Vit + 1/2at^2
x = Vft + 0

i don't know how to figure these out...
d.) would the amount of time increse becasue it has less mass??
e.) would x increase because it has more time to fall??

Thanks for any help!!

2. Dec 1, 2006

### Staff: Mentor

That's the first step. Keep going. (Don't leave your answer in terms of Vf.)

Well? Solve for the horizontal distance. (Please use different letters to represent horizontal and vertical motion.)

You may as well solve these before worrying about d and e. But the hint for those two is: Does the block end up going faster or slower than in the earlier case.

3. Dec 1, 2006

Is this right??
a.) Vf = (mVo)/(m+100m)
(mVo)/m(1+100)
Vo/101

b.) 1/2(m+100m)(Vf)^2 - 1/2mVo^2 = change in KE
1/2(m+100m)(Vo/101)^2 - 1/2mVo^2 = change in KE
1/2m(101)(Vo/101)^2 - 1/2mVo^2 = change in KE
1/2m(Vo)^2 - 1/2mVo^2 = change in KE
0 = change in KE
can that be right?

4. Dec 1, 2006

### arildno

Is $\frac{101}{(101)^{2}}=1??$

5. Dec 1, 2006

no

i'm so confused

6. Dec 1, 2006

### arildno

So why did you state that it was, when going from the 7th line to your 8th line in your previous post?

Aside from that silly little mistake, your work looks good!

7. Dec 1, 2006

1/2m(101)(Vo/101)^2 - 1/2mVo^2 = change in KE
1/2m(Vo)^2 - 1/2mVo^2 = change in KE

so you can't cancel the 101?

8. Dec 1, 2006

### Staff: Mentor

Good.
You made a mistake simplifying the term that I bolded in red. (As arildno has pointed out.)

9. Dec 1, 2006

### Staff: Mentor

You can cancel one of them. (Don't forget the square!)

10. Dec 1, 2006

oh, i see.
so it would be 1/2m(Vo^2/101) - 1/2mVo^2

11. Dec 1, 2006

### Staff: Mentor

Good. Now simplify it.

12. Dec 1, 2006

1/2mVo^2(-100/101) = change in KE

13. Dec 1, 2006

for c.) can't i just use Vf=(Vo/101)
x=(Vf)t
x=(Vo/101)t

14. Dec 1, 2006

### Staff: Mentor

Simplify it further.

Nothing wrong with that as a first step, but you can't stop there. (You can't just leave an unknown "t" in your answer.) Now write the equation for the vertical motion and solve both equations simultaneously.

15. Dec 1, 2006

y = Vt + 1/2at^2
h = 0 + 1/2(-10)t^2
t = square root of (h/-5)

x = (Vo/101)(square root of (h/-5))

16. Dec 1, 2006

### Staff: Mentor

You realize that square roots of negative numbers presents a problem, right?

If you take the acceleration as a = -10 m/s^2; then the final height is y = -h (since it falls a distance h).

17. Dec 1, 2006

Thanks for all the help!
I appriciate it!

18. Dec 2, 2006

I have been thinking about parts d and e, and this is what I have decided:

d.) y = 1/2at^2
-h = 1/2(-10)t^2
t = square root of (h/5)
Since the height doesn't change, the time it takes for the block to fall would stay the same.

e.) Since momentum had to be conserved, the velocity of the block would be less if the bullet went through the block.
x = Vt
t = square root of (h/5)
That would mean that the distance would have to be smaller.

Is this correct?

19. Dec 2, 2006

### Hootenanny

Staff Emeritus
Please ignore sherlock, she is simply a secretary practising her typing and p#ssing everyone off :grumpy:

20. Dec 2, 2006

### Moonbear

Staff Emeritus
Thanks, Hootenanny, for pointing that out so pinkpolkadots would not be further confused.