Solving for Final Momentum and Velocity of a Baseball-Bullet Collision

[domyy]

Homework Statement

A baseball pitcher throws a fast-ball (mass 50g) to stop a bullet (mass 5g), which has been shot at him at a speed of 400m/s by an angry fan. Can the pitcher save himself by stopping the bullet with a fast-ball of 100mph assuming a perfectly inelastic head-on collision, where the bullet gets stuck in the baseball?

What is the final momentum and the final speed of the baseball+bullet system?

Homework Equations

P = mv+mv

The Attempt at a Solution

So I did:

Final momentum:

P= bullet = (400m/s)(0.005kg) = 2

p = fast-ball = 100mph = 44.7m/s = (44.7m/s)(0.05kg) = 2.235

Pf = 2.235 + 2 = 4.235kg.m/s

Final velocity:

If the question were find the final velocity of the bullet, I guess I´d have written 0, right (because it´s perfectly inelastic)?

But since I am being asked the final speed for both baseball +bullet system, I am attempting:

v = p/m
v = 4.235kg.m/s divided by 0.055kg (total mass) = 77m/s.

So, is that correct?

 

[tal444]

You are right all the way up to the point where you get your Pf. That is incorrect, as the momentum is in opposite directions. You should subtract, not add.

 

[domyy]

So,

pf = 0.235kg. m/s

vf = v/m = 0.235kg. m/s divided by 0.055kg (total mass) = 4.27m/s.

Is that correct now?

 

[tal444]

Yes. So what can we conclude from your answers? The pitcher can indeed save himself from the bullet. Don't try this at home though, it's a crazy physics question :P.

 

[domyy]

hahaha! Thank you SO MUCH! You are great ! =)

 

[tal444]

Np, glad I could help :)