Inelastic Momentum?

Question

A magician attempts to catch a bullet with his teeth. The mass of the bullet is 15 grams and its initial speed is 200 m/s as it leaves the gun.

1. Calculate the final speed of the combined mass of his skull (6 kg) and the bullet, assuming that his head starts from rest.

2. If his head acquires this new speed in a movement of 5 cm, calculate the acceleration that his head must undergo in g's.

My answers:

1. .499 m/s

2. Acceleration comes out to (-2.49 m/s^2) which is equal to .2541 g's.

Am I right? Thanks.

Answer 1

1.)using conservation of momentum

200*15/1000=(6+15/1000)*v
v=0.499 m/s

2.) relating s and a where s=5 cm
5/100=.5*a*t^2
and
0.499=a*t

combining
10/100=0.499*t
t=0.20 seconds
a=2.49 m/s^2
which is
0.254 g

you are correct

j