You are a worldfamous physicistlawyer defending a client who

You are a world-famous physicist-lawyer defending a client who has been charged with murder. It is alleged that your client, Mr. Smith, shot the victim, Mr. Wesson. The detective who investigated the scene of the crime found a second bullet, from a shot that missed Mr Wesson, that had embedded itself into a chair. You arise to cross-examine the detective. You: In what type of chair did you find the bullet? Det: A wooden chair. You How massive was this chair? Det: It had a mass of 20.0 kg. You: How did the chair respond to being struck with a bullet? Det: It slid across the floor. You: How far? Det: Three centimeters. The slide marks on the dusty floor are quite distinct. You: What kind of floor was it? Det: A wood floor, very nice oak planks. You: What was the mass of the bullet you retrieved from the chair? Det: Its mass was 10 g. You: And how far had it penetrated into the chair? Det: A distance of 7.00 cm. You: Have you tested the gun you found in Mr. Smith\'s possession? Det I have. You: What is the muzzle velocity of bullets fired from that gun? Det: The muzzle velocity is 450 m/s You: And the barrel length? Det: The gun has a barrel length of 62 cm.

Solution

momentum of bullet = m*v = 0.010*450= 4.5 kg.m/sec

momentum conservation

Pi = Pf

4.5 = 20*v

v = 4.5/20 = 0.225 m/sec

now Kf = 0.5*20*0.225^2 = 0.5062 J

By work-energy theoram

KE = umgd

u is coeficient of kinetic friction

0.5062 = 0.2*20*9.81*d

d = 0.5062/(0.2*20*9.81) = 0.0129 m

d = 1.29 cm

correct distance will be = 1.29 cm