/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 57 A bullet is fired through a boar... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 57

A bullet is fired through a board \(10.0 \mathrm{~cm}\) thick in such a way that the bullet's line of motion is perpendicular to the face of the board. If the initial speed of the bullet is \(400 \mathrm{~m} / \mathrm{s}\) and it emerges from the other side of the board with a speed of \(300 \mathrm{~m} / \mathrm{s}\), find (a) the acceleration of the bullet as it passes through the board and (b) the total time the bullet is in contact with the board.

Short Answer

Expert verified
From the calculations, (a) The bullet has a deceleration of 500,000 m/s虏 while passing through the board. (b) The time of contact between the bullet and board is 0.0002 seconds.

Step by step solution

01

Calculating deceleration

The initial and final velocities are given, as well as the distance over which the bullet slows down. We can use the second equation of motion, \(v^2 = u^2 + 2as\), to find the deceleration \(a\), where \(v\) is the final velocity, \(u\) is the initial velocity, and \(s\) is the distance. Rearranging yields \( a = (v^2 - u^2) / 2s \). Substituting the given values gives \( a = ((300 m/s)^2 - (400 m/s)^2) / (2 * 0.1 m) \).
02

Calculating contact time

Once we know the acceleration, we can find the time it takes for the bullet to go through the board. Here we use the first equation of motion, \( v = u + at \), which rearranged gives \( t = (v - u) / a\). Substituting our previously calculated acceleration and given velocities, we get \( t = (300 m/s - 400 m/s) / acceleration \).

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