As shown in the figure below, a bullet is fired at and passes through a piece of

Question

As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.456)v after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.433)KEb BC] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.)

V=___v

M=___m

Explanation / Answer

[KEb BC]= 0.5 * m* v2

now after collsion the kinetic energy = 0.5* m* ( (0.456)v)2

= 0.2079 *[KEb BC]

now,

energy lost =[(0.433)KEb BC]

the energy lost is gained by target

= (1-0.433-0.208)[KEb BC]

= 0.359[KEb BC]= 0.5*M*V2  

=  0.359 *0.5*m*v2= 0.5*M*V2 .....................(1) ( KE in terms of target)

now, we use conservation of momentum,

mv=0.456mv + MV

=>MV=0.544mv ...............(2)

putting (2) in (1) we get,

=>0.359mv2= 0.554 mv*V

=>V= 0.648 v

now, putting V in eq (2) we get ,

MV=0.544mv

=>M*0.648 v= 0.544mv

=>M=0.8395 m

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