Calculating Bullet Speed in Momentum Problem

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To find the bullet's speed when it embeds into a block and causes it to slide, the conservation of momentum and the work-energy principle are applied. The bullet's speed can be expressed as v(bullet) = Msqrt(2μkgd)/m, where m is the bullet's mass, M is the block's mass, μk is the coefficient of kinetic friction, and d is the distance slid. The equation accounts for the kinetic friction acting on the block after the collision. It's important to include the mass of the bullet in the calculations to ensure accuracy. This approach effectively combines momentum and friction concepts to solve the problem.
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Homework Statement


A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is μk.

Find an expression for the bullet's speed vbullet.
Express your answer in terms of the variables m, M, μk, d, and appropriate constants.

Homework Equations


p=mv

The Attempt at a Solution



v(bullet)=Msqrt(2μkgd)/m
 
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You should show the steps you took to arrive at your answer.
 
got it, forgot to include the mass of the bullet
 

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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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