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 (0.556)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 [(0.403)K, Bc), that is, 0.403 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 = M = m M (a) Before collision (b) After collision

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 (0.556)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 [(0.403)K, Bc), that is, 0.403 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 = M = m M (a) Before collision (b) After collision

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Description: 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 \( (0.556)v \) after passing t

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter8: Momentum And Collisions

Section: Chapter Questions

Problem 1OQ

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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 \( (0.556)v \) 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 \([ (0.403)K_{b \, BC} ]\), that is, \(0.403\) 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.)

\[ V = \,\, \, \, \, \, \]

\[ M = \,\, \, \]

**Diagrams:**

There are two parts to the diagram:

- **(a) Before collision:**
- The bullet with mass \(m\) is depicted moving towards the target with a velocity \(v\).
- The target, with a mass \(M\), is suspended and initially stationary.

- **(b) After collision:**
- The bullet moves past the target with a reduced speed of \(0.556v\).
- The target is now moving with a velocity \(V\).

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