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 (0.506)v after passing through the target. The collision is inelastic and during the collision, the amount of kinetic energy lost by the bullet and paper is equal to [(0.333)Kb BC], that is, 0.333 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

edit: updated quesion so it would be clearer.

Explanation / Answer

By Conservation of momentum

mv =MV+mVf

mv=MV+m(0.506)v

0.494mv=MV

By Conservation of energy

(1/2)mv2 =(1/2)MV2+(1/2)m(0.506v)2+0.333*(1/2)mv2

0.411mv2=MV2 =(MV)V

0.411mv2=(0.494mv)V

V=0.832v

Therefore

=>0.494mv =M(0.832v)

M=0.5938m

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