A bullet is fired at and passes through a piece of target paper suspended by a m

Question

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

(0.546)v

after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction

[(0.383)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

Let the system consist of the bullet and the paper. Since momentum in the system is conserved. Let mass of bullet be m and mass of paper be M. Let v be initial speed of bullet.

p_f = p_i
M*v_paper + m*0.546v = mv

For conservation of Energy,

?E = ?transferred energy
KE_f - KE_i = energy transferred
1/2m(0.546v)^2 + 1/2M(v_paper)^2 - 1/2mv^2 = -0.383*1/2mv^2

Using,

The equations u have now are sufficient for the answer

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