Question

A bullet flies horizontally, hits a wooden block suspended from a 1.0 m string, and gets stuck in the block. The angle of deviation of the string equals 11 degrees. The mass of the bullet is 1000 times smaller than the mass of the block. What is the initial speed of the bullet? Point out the laws of physics in the solution and show all steps.

Answer 1

first we need to calculate the velocity just after bullet stuck in the wooden box for it we need to apply momentum conservation  

suppose mass of wooden box = m then mass of bullet m/1000

Pi= Pf

m*v for bullet = m*vc for common bullet and box

m/1000 * V = (m+ m/1000) * Vc ....................1

i assume bullet initial velocity = v and for bullet and box together just after hitting =vc

just after bullet stuck into wooden box bullet has energy and this energy will raise the system to some height  

so apply energy conservation here

KEi + PEi = KEf + PEf

1/2* ( m+ m/1000) *Vc^2 = ( m+ m/1000) * g*L*( 1-cos11)

L = 1 m lenght of string

from here Vc = sqrt( 2*g*L* (1-cos(11))

= sqrt( 2*9.8*1 *(1-cos11)) = 0.600089 m/s

put this into first eqution

m/1000 * V = (m+ m/1000) * Vc

1/1000*V = ( 1+1/1000) *0.600089

from here we got V = 600.689 m/s

laws of physics = energy conservation (just after bullet transfer its kinetic energy ) and momentum conservation

let me know in comment if u need further explanation