What Is the Exit Velocity of a Projectile After Passing Through a Wooden Block?

[shawonna23]

A 0.165 kg projectile is fired with a velocity of +705 m/s at a 2.00 kg wooden block that rests on a frictionless table. The velocity of the block, immediately after the projectile passes through it, is +55.0 m/s. Find the velocity with which the projectile exits from the block.

I used the equation vf1=(m1-m2)/(m1+m2) but I got the wrong answer. Can you please help me?

 

[lalbatros]

Conservation of momentum is the answer.

Before the impact, the total momentum is:

0.165 * 705 + 0 * 0 kg m/s (bullet + wood)

After the impact, the total momentum is (vp is the bullet residual velocity):

0.165 * vp + 2 * 55 kg m/s (bullet + wood)

Since momentum is conserved, these two momentum should be equal:

0.165 * 705 + 0 * 0 = 0.165 * vp + 2 * 55

You can solve this equation for vp and get the result.

You can check that the bullet final velocity is 38.33 m/s (right ?) since:

0.165 * 705 + 0 * 0 = 0.165 * 38.33 + 2 * 55

(hint: never apply an equation, apply the principles)

 

[saiakhil]

A 0.165 kg projectile is fired with a velocity of +705 m/s at a 2.00 kg wooden block that rests on a frictionless table. The velocity of the block, immediately after the projectile passes through it, is +55.0 m/s. Find the velocity with which the projectile exits from the block.

I used the equation vf1=(m1-m2)/(m1+m2) but I got the wrong answer. Can you please help me?

Try using law of conservation of momentum i.e.

mv₁+MV₁=mv₂+MV₂
By using it we get velocity of projectile as 38.33

 

[xts]

First of all:
Forum Rules: Do not post your homework/school-type questions here!

So here you may got a common sense physics answer rather than a solution to most unrealistic school exercise:
1. there is no such thing as 'frictionless table';
2. "0.165 kg projectile is fired with a velocity of 705 m/s" means you deal with a bullet of heaviest (20mm) machine gun;
3. have you ever seen a wooden plank hit by a rifle bullet? So try to imagine what may remain after being hit by 20mm bullet, then try to count the splinters and estimate momentum carried by them; If you haven't seen - watch Discovery Channel military programmes ;)
4. If you listen to answers like "velocity of projectile as 38.33" try to picture it - the bullet 'passes through it...exits from the block' at the speed lower than block has itself.

EDITED>>>
Sorry - I've underestimated caliber. Heaviest 20mm bullets have only 0.11 kg.
0.165kg may be an armour-piercing bullet for 25mm cannons, used in assault helicopters. Their typical muzzle velocity is 720m/s.
So now picture yourself a wooden block hit by such bullet...