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

(0.526)v

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

[(0.453)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.)

Explanation / Answer

let mass of target be M
speed of target at instant of collision = V
then from conservation of momentum, initial momentum = final momentum
mu = mv' + MV
mv = m(0.526v) + MV

also, mv^2 - m(0.526)^2 - MV^2 = 2*0.453*mv^2
V = sqroot( [0.094mv^2 - 0.276m]/M)

so, mv = 0.526mv + Msqroot( [0.094mv^2 - 0.276m]/M)
0.474mv = Msqroot( [0.094mv^2 - 0.276m]/M)
0.2246 m v^2 /[[0.094v^2 - 0.276]]= M

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